Search: id:A040977
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%I A040977
%S A040977 1,8,35,112,294,672,1386,2640,4719,8008,13013,20384,30940,45696,65892,
%T A040977 93024,128877,175560,235543,311696,407330,526240,672750,851760,1068795,
%U A040977 1330056,1642473,2013760,2452472,2968064,3570952,4272576,5085465
%N A040977 C(n+5,5)*(n+3)/3
%C A040977 Sequence is n^2*(n^2-1)*(n^2-4)/360 if offset 3.
%C A040977 If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then 
               a(n-7) is the number of 7-subsets of X intersecting both Y and Z. 
               - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
%C A040977 6-dimensional square numbers, fifth partial sums of binomial transform 
               of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+5,i+5)*b(i)}, where b(i)=[1,
               2,0,0,0,...]. [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), 
               Mar 05 2009]
%C A040977 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 
               2009: (Start)
%C A040977 Sequence of the absolute values of the z^2 coefficients divided by 5 
               of the polynomials in the GF2 denominators of A156925. See A157703 
               for background information.
%C A040977 (End)
%D A040977 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pp. 194-196.
%D A040977 Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical 
               Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.
%H A040977 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A040977 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A040977 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A040977 a(n)= ((-1)^n)*A053120(2*n+6, 6)/32 ( 1/32 of seventh unsigned column 
               of Chebyshev T-triangle, zeros omitted).
%F A040977 G.f.: (1+x)/(1-x)^7.
%F A040977 a(n-3) = sum(i+j+k=n, i*j*k^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Nov 01 2002
%F A040977 a(n)=2*C(n+6, 6)-C(n+5, 5). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003
%F A040977 a(n-3) = 1/(1!*2!*3!)*sum {1 <= x_1, x_2, x_3 <= n} |det V(x_1,x_2,x_3)| 
               = 1/12*sum {1 <= i,j,k <= n} |(i-j)(i-k)(j-k)|, where V(x_1,x_2,x_3} 
               is the Vandermonde matrix of order 3. - Peter Bala (pbala(AT)toucansurf.com), 
               Sep 13 2007
%F A040977 a(n)=C(n+5,5)+2*C(n+5,6) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), 
               Mar 05 2009]
%p A040977 with(combinat); A040977 := n->binomial(n+5,5)*(n+3)/3;
%p A040977 a:=n->(sum((numbcomp(n,6)), j=4..n))/3:seq(a(n), n=6..38);# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
%p A040977 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 
               2009: (Start)
%p A040977 nmax:=34; for n from 0 to nmax do fz(n):=product((1-m*z)^(n+1-m),m=1..n); 
               c(n):= abs(coeff(fz(n),z,2))/5; end do: a:=n-> c(n): seq(a(n), n=2..nmax);
%p A040977 (End)
%t A040977 s1=s2=s3=s4=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst,
               s4],{n,0,7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 15 2009]
%Y A040977 Partial sums of A005585. Cf. A050486.
%Y A040977 Cf. A000292, A133111, A133112.
%Y A040977 Cf. A005585 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 
               2009]
%Y A040977 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 
               2009: (Start)
%Y A040977 Cf. A156925, A157703
%Y A040977 (End)
%Y A040977 Sequence in context: A058102 A006600 A005732 this_sequence A036598 A059824 
               A094616
%Y A040977 Adjacent sequences: A040974 A040975 A040976 this_sequence A040978 A040979 
               A040980
%K A040977 easy,nonn
%O A040977 0,2
%A A040977 Barry E. Williams, Dec 14 1999
%E A040977 More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 26 2000

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