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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
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
KEYWORD
nonn
AUTHOR
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.)