%I M4280 #33 Jul 09 2021 17:34:18

%S 1,1,6,72,1322,32550,1003632,37162384,1605962556,79330914540,

%T 4409098539560,272297452742304,18499002436677336,1371050716542451672,

%U 110085169034456183232,9519063815009322326400,881914870734754844035088,87154631117420724492647184

%N a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k)*C(k^2,n).

%D H. W. Gould, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A003235/b003235.txt">Table of n, a(n) for n = 0..300</a>

%H Henry W. Gould, <a href="/A003099/a003099.pdf">Letters to N. J. A. Sloane, Oct 1973 and Jan 1974</a>.

%F 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

%F A003236(n) / a(n) ~ -2 / LambertW(-2*exp(-2)) = 4.92155363456750509... - _Vaclav Kotesovec_, Jul 09 2021

%t Table[Sum[(-1)^(n-k) * Binomial[n,k] * Binomial[k^2, n], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Dec 13 2020 *)

%Y Cf. A346184.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Mar 19 2015