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A005260
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Sum C(n,k)^4, k = 0 . . n.
(Formerly M2110)
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6
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1, 2, 18, 164, 1810, 21252, 263844, 3395016, 44916498, 607041380, 8345319268, 116335834056, 1640651321764, 23365271704712, 335556407724360, 4854133484555664, 70666388112940818, 1034529673001901732
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| 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).
G.f.: 5*hypergeom([1/8, 3/8],[1], (4/5)*((1-16*x)^(1/2)+(1+4*x)^(1/2))*(-(1-16*x)^(1/2)+(1+4*x)^(1/2))^5/(2*(1-16*x)^(1/2)+3*(1+4*x)^(1/2))^4)^2/(2*(1-16*x)^(1/2)+3*(1+4*x)^(1/2)) - Mark van Hoeij, Oct 29 2011.
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PROG
| (PARI) sum(k=0, n, binomial(n, k)^4)
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CROSSREFS
| Cf. A000172, A096192.
Sequence in context: A144513 A037518 A037721 * A183250 A037728 A037623
Adjacent sequences: A005257 A005258 A005259 * A005261 A005262 A005263
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Michael Somos, Aug 09, 2002
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