0,2

Sequence is n^2*(n^2-1)*(n^2-4)/360 if offset 3.

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

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]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)

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.

(End)

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.

Index entries for sequences related to linear recurrences with constant coefficients

Milan Janjic, Two Enumerative Functions

Index entries for sequences related to Chebyshev polynomials.

a(n)= ((-1)^n)*A053120(2*n+6, 6)/32 ( 1/32 of seventh unsigned column of Chebyshev T-triangle, zeros omitted).

G.f.: (1+x)/(1-x)^7.

a(n-3) = sum(i+j+k=n, i*j*k^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 01 2002

a(n)=2*C(n+6, 6)-C(n+5, 5). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003

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

a(n)=C(n+5,5)+2*C(n+5,6) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]

with(combinat); A040977 := n->binomial(n+5, 5)*(n+3)/3;

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]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)

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);

(End)

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]

Partial sums of A005585. Cf. A050486.

Cf. A000292, A133111, A133112.

Cf. A005585 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)

Cf. A156925, A157703

(End)

Sequence in context: A058102 A006600 A005732 this_sequence A036598 A059824 A094616

Adjacent sequences: A040974 A040975 A040976 this_sequence A040978 A040979 A040980

easy,nonn

Barry E. Williams, Dec 14 1999

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 26 2000