%I #11 Feb 18 2022 12:58:43
%S 1,1,13,630,65446,11732175,3222746276,1257489289280,661150527657180,
%T 450529025613124095,386183537239831846450,406654820487854059966416,
%U 516014868401631381045209376,776565429016998902169538130936
%N a(n) = [x^n] Product_{k=1..n} (1 + k*x)^n.
%F a(n) ~ exp(n + 1/3) * n^(2*n - 1/2) / (sqrt(Pi) * 2^(n + 1/2)). - _Vaclav Kotesovec_, Feb 18 2022
%t Table[SeriesCoefficient[Product[(1 + k*x)^n, {k,1,n}], {x,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Feb 18 2022 *)
%o (PARI) a(n) = polcoef(prod(k=1, n, 1+k*x)^n, n);
%Y Cf. A000142, A129256, A351508.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 12 2022
|