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 A003236 a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k)*C((k+1)^2, n). (Formerly M3107) 3
 1, 3, 24, 320, 6122, 153762, 4794664, 178788528, 7762727196, 384733667780, 21434922419504, 1326212860090560, 90227121642144424, 6694736236093168200, 538028902298395832832, 46558260925421295229568, 4316186393637505403773328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES H. W. Gould, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 Henry W. Gould, Letters to N. J. A. Sloane, Oct 1973 and Jan 1974. FORMULA a(n) ~ c * d^n * (n-1)!, where d = 4 / (w*(2-w)) = 6.17655460948348035823168... and c = exp(1/2 - w^2/8) / (Pi*sqrt(2*w*(1-w))) = 0.740112385268663459927202070799244309431121698475089032623558890186368006364..., where w = -LambertW(-2*exp(-2)) = -A226775. - Vaclav Kotesovec, Dec 13 2020, updated Jul 09 2021 a(n) / A003235(n) ~ -2 / LambertW(-2*exp(-2)) = 4.92155363456750509... - Vaclav Kotesovec, Jul 09 2021 MATHEMATICA Table[Sum[(-1)^(n-k) * Binomial[n, k] * Binomial[(k+1)^2, n], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 13 2020 *) CROSSREFS Cf. A346183. Sequence in context: A047056 A343445 A264561 * A232693 A319939 A082166 Adjacent sequences: A003233 A003234 A003235 * A003237 A003238 A003239 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Sean A. Irvine, Mar 19 2015 STATUS approved

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Last modified May 20 08:05 EDT 2024. Contains 372703 sequences. (Running on oeis4.)