Search: id:A005260
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%I A005260 M2110
%S A005260 1,2,18,164,1810,21252,263844,3395016,44916498,607041380,8345319268,
%T A005260 116335834056,1640651321764,23365271704712,335556407724360,
%U A005260 4854133484555664,70666388112940818,1034529673001901732
%N A005260 Sum C(n,k)^4, k = 0 . . n.
%D A005260 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005260 F. Beukers, Another congruence for the Apery numbers. J. Number Theory 
               25 (1987), no. 2, 201-210.
%D A005260 C. Elsner, On recurrence formulae for sums involving binomial coefficients, 
               Fib. Q., 43 (No. 1, 2005), 31-45.
%D A005260 H. W. Gould, Combinatorial Identities, Morgantown, 1972, (X.14), p. 79.
%H A005260 V. Strehl, <a href="http://www.mat.univie.ac.at/~slc/opapers/s29strehl.html">
               Recurrences and Legendre transform</a>
%H A005260 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BinomialSums.html">Link to a section of The World of Mathematics.</
               a>
%F A005260 a(n) ~ 2^(1/2)*pi^(-3/2)*n^(-3/2)*2^(4*n) - Joe Keane (jgk(AT)jgk.org), 
               Jun 21 2002
%F A005260 n^3a(n) = 2(2n-1)(3n^2-3n+1)a(n-1) + (4n-3)(4n-4)(4n-5)a(n-2).
%o A005260 (PARI) sum(k=0,n,binomial(n,k)^4)
%Y A005260 Cf. A000172, A096192.
%Y A005260 Sequence in context: A144513 A037518 A037721 this_sequence A037728 A037623 
               A052865
%Y A005260 Adjacent sequences: A005257 A005258 A005259 this_sequence A005261 A005262 
               A005263
%K A005260 nonn,easy
%O A005260 0,2
%A A005260 N. J. A. Sloane (njas(AT)research.att.com).
%E A005260 Edited by Michael Somos, Aug 09, 2002

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