|
%I #12 Sep 23 2018 16:29:42
%S 1,1,8,54,496,5400,73728,1204322,23167808,512093178,12781430600,
%T 355128859129,10863077554224,362572265689777,13107541496092960,
%U 510105773344747725,21258690342206888192,944467894258279964254,44555341678790400325512,2224158766859058600584834,117123916650423288611260400
%N a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^k)^k.
%H Vaclav Kotesovec, <a href="/A298985/b298985.txt">Table of n, a(n) for n = 0..380</a>
%F a(n) ~ n^n. - _Vaclav Kotesovec_, Feb 02 2018
%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(binomial(i+j-1, j)*b(n-i*j, i-1, k)*k^j, j=0..n/i)))
%p end:
%p a:= n-> b(n$3):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 23 2018
%t Table[SeriesCoefficient[Product[1/(1 - n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%Y Cf. A000219, A124577, A261561, A261565, A266941, A297329, A298986, A298987, A298988.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 31 2018
|
