%I #13 Aug 01 2019 13:12:06
%S 1,1,5,28,137,726,3896,21071,115089,633007,3500740,19448573,108458924,
%T 606787572,3404112479,19142919543,107874784017,609021410570,
%U 3443952349385,19503777943838,110599636109572,627924447630011,3568885868192419,20304321490356084
%N a(n) = [x^n] Product_{k>=1} (1 + k*x^k)^n.
%H Robert Israel, <a href="/A297322/b297322.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A297321(n,n).
%F a(n) ~ c * d^n / sqrt(n), where d = 5.814548482877687529318372516965305077397562... and c = 0.2563102401728134539247148322678842806264... - _Vaclav Kotesovec_, Aug 01 2019
%p f:= proc(n) local k;
%p coeff(series(mul((1+k*x^k)^n,k=1..n),x,n+1),x,n);
%p end proc:
%p map(f, [$0..30]); # _Robert Israel_, Dec 28 2017
%t Table[SeriesCoefficient[Product[(1 + k x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 24}]
%Y Main diagonal of A297321.
%Y Cf. A297324, A297326, A297329.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 28 2017