OFFSET
0,3
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) / (2*Pi*sqrt(2*(1-w)/w)) = 0.150381859108542022051646532351211728293419626579836320368956458003898775818..., where w = -LambertW(-2*exp(-2)) = -A226775. - Vaclav Kotesovec, Dec 13 2020, updated Jul 09 2021
A003236(n) / a(n) ~ -2 / LambertW(-2*exp(-2)) = 4.92155363456750509... - Vaclav Kotesovec, Jul 09 2021
MATHEMATICA
Table[Sum[(-1)^(n-k) * Binomial[n, k] * Binomial[k^2, n], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 13 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Mar 19 2015
STATUS
approved