%I A003472 M4718
%S A003472 1,10,60,280,1120,4032,13440,42240,126720,366080,1025024,2795520,
%T A003472 7454720,19496960,50135040,127008768,317521920,784465920,1917583360,
%U A003472 4642570240,11142168576,26528972800,62704844800,147220070400
%N A003472 2^(n-4)*C(n,4).
%C A003472 Number of 4D hypercubes in n-dimensional hypercube - Henry Bottomley 
               (se16(AT)btinternet.com), Apr 14 2000.
%C A003472 With four leading zeros, binomial transform of C(n,4) - Paul Barry (pbarry(AT)wit.ie), 
               Apr 10 2003
%C A003472 If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for 
               n>3, a(n) is equal to the number of (n+4)-subsets of X intersecting 
               each X_i (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Jul 
               21 2007
%C A003472 With a different offset, number of n-permutations (n=5) of 3 objects: 
               u, v, z, with repetition allowed, containing exactly four (4) u's. 
               Example: a(1)=10 because we have uuuuv uuuvu uuvuu uvuuu vuuuu uuuuz 
               uuuzu uuzuu uzuuu zuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 12 2008
%D A003472 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003472 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A003472 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 796.
%D A003472 Jones, C. W.; Miller, J. C. P.; Conn, J. F. C.; Pankhurst, R. C.; Tables 
               of Chebyshev polynomials. Proc. Roy. Soc. Edinburgh. Sect. A. 62, 
               (1946). 187-203.
%D A003472 H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 
               74 (1970), 56-62.
%H A003472 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A003472 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A003472 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003472 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A003472 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A003472 a(n)=2*a(n-1)+A001789(n-1)
%F A003472 G.f. 1/(1-2x)^5 E.g.f. exp(2x)(x^4/4!) (with 4 leading zeros) - Paul 
               Barry (pbarry(AT)wit.ie), Apr 10 2003
%p A003472 A003472:=-1/(2*z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
%p A003472 seq(binomial(n+4,4)*2^n,n=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 12 2008
%o A003472 (Other) SAGE: [lucas_number2(n, 2, 0)*binomial(n,4)/16for n in xrange(4, 
               28)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 
               2009]
%Y A003472 Cf. A001787, A001788, A001789.
%Y A003472 Sequence in context: A144560 A076160 A004406 this_sequence A112502 A083585 
               A155633
%Y A003472 Adjacent sequences: A003469 A003470 A003471 this_sequence A003473 A003474 
               A003475
%K A003472 nonn,easy,nice
%O A003472 4,2
%A A003472 N. J. A. Sloane (njas(AT)research.att.com).
%E A003472 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000