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A371487 Expansion of e.g.f. Product_{k>=2} 1 / (1 - x^k/k).

%I A371487 #8 Mar 26 2024 11:15:38
%S A371487 1,0,1,2,12,44,380,2064,20888,166368,1872792,18917040,253473792,
%T A371487 3042859104,45895372224,661334985024,11073993828480,182021308975104,
%U A371487 3418263102400128,63023443312105728,1302276954815368704,26806365139264980480,603186053115872024064,13651035149069305878528
%N A371487 Expansion of e.g.f. Product_{k>=2} 1 / (1 - x^k/k).
%p A371487 with(combinat):
%p A371487 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0, add(
%p A371487      (i-1)!^j*b(n-i*j, i-1)*multinomial(n, n-i*j, i$j), j=0..n/i)))
%p A371487     end:
%p A371487 a:= n-> b(n$2):
%p A371487 seq(a(n), n=0..23);  # _Alois P. Heinz_, Mar 26 2024
%t A371487 nmax = 23; CoefficientList[Series[Product[1/(1 - x^k/k), {k, 2, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y A371487 Cf. A007841, A371485, A371493.
%K A371487 nonn
%O A371487 0,4
%A A371487 _Ilya Gutkovskiy_, Mar 25 2024