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Search: id:A005260
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| A005260 |
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Sum C(n,k)^4, k = 0 . . n.
(Formerly M2110)
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+0
5
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| 1, 2, 18, 164, 1810, 21252, 263844, 3395016, 44916498, 607041380, 8345319268, 116335834056, 1640651321764, 23365271704712, 335556407724360, 4854133484555664, 70666388112940818, 1034529673001901732
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
F. Beukers, Another congruence for the Apery numbers. J. Number Theory 25 (1987), no. 2, 201-210.
C. Elsner, On recurrence formulae for sums involving binomial coefficients, Fib. Q., 43 (No. 1, 2005), 31-45.
H. W. Gould, Combinatorial Identities, Morgantown, 1972, (X.14), p. 79.
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LINKS
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V. Strehl, Recurrences and Legendre transform
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) ~ 2^(1/2)*pi^(-3/2)*n^(-3/2)*2^(4*n) - Joe Keane (jgk(AT)jgk.org), Jun 21 2002
n^3a(n) = 2(2n-1)(3n^2-3n+1)a(n-1) + (4n-3)(4n-4)(4n-5)a(n-2).
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PROGRAM
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(PARI) sum(k=0, n, binomial(n, k)^4)
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CROSSREFS
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Cf. A000172, A096192.
Sequence in context: A144513 A037518 A037721 this_sequence A037728 A037623 A052865
Adjacent sequences: A005257 A005258 A005259 this_sequence A005261 A005262 A005263
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Michael Somos, Aug 09, 2002
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