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A003162
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A binomial coefficient summation.
(Formerly M2597)
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2
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1, 1, 1, 3, 6, 19, 49, 163, 472, 1626, 5034, 17769, 57474, 206487, 688881, 2508195, 8563020, 31504240, 109492960, 406214878, 1432030036, 5349255726, 19077934506, 71672186953, 258095737156, 974311431094, 3537275250214, 13408623649893
(list;
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history;
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OFFSET
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0,4
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REFERENCES
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Problem E2384, Amer. Math. Monthly, 81 (1974), 170-171.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=0..27.
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FORMULA
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G.f.: hypergeometric expression with an anti-derivative, see Maple program - Mark van Hoeij, May 06 2013
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MAPLE
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H := hypergeom([1/2, 1/2], [1], 16*x^2);
ogf := (Int(6*H*(4*x^2+5)/(4-x^2)^(3/2), x)+H*(16*x^2-1)/(4-x^2)^(1/2))*((2-x)/(2+x))^(1/2)/(4*x)+1/(8*x);
series(ogf, x=0, 20); # Mark van Hoeij, May 06 2013
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PROG
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(PARI) a(n)=if(n<0, 0, sum(k=0, n\2, (binomial(n, k)-binomial(n, k-1))^3)/binomial(n, n\2)) /* Michael Somos, Jun 02 2005 */
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CROSSREFS
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Cf. A003161.
Sequence in context: A148566 A148567 A148568 * A179277 A129417 A132335
Adjacent sequences: A003159 A003160 A003161 * A003163 A003164 A003165
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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