A363010 - OEIS

%I #21 May 12 2023 16:26:33

%S 1,1,4,36,594,15775,618838,33757864,2448904188,228290728635,

%T 26617527649365,3797508644987398,651082351708066303,

%U 132130157056046918808,31333332827346731906130,8587011712002719806274022,2693586800519167315881703732,958983405298849163873718493941

%N a(n) = n! * [x^n] 1/(1 - f^n(x)), where f(x) = exp(x) - 1.

%H Alois P. Heinz, <a href="/A363010/b363010.txt">Table of n, a(n) for n = 0..246</a>

%F a(n) = T(n,n), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = n!.

%p b:= proc(n, t, m) option remember; `if`(n=0, `if`(t<2, m!,

%p       b(m, t-1, 0)), m*b(n-1, t, m)+b(n-1, t, m+1))

%p     end:

%p a:= n-> b(n$2, 0):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, May 12 2023

%Y Main diagonal of A363007.

%Y Main diagonal of A153278 (for n>=1).

%Y Cf. A139383, A261280, A346802, A351433.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 12 2023