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

1, 0, 1, 2, 12, 44, 380, 2064, 20888, 166368, 1872792, 18917040, 253473792, 3042859104, 45895372224, 661334985024, 11073993828480, 182021308975104, 3418263102400128, 63023443312105728, 1302276954815368704, 26806365139264980480, 603186053115872024064, 13651035149069305878528

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0, add(
     (i-1)!^j*b(n-i*j, i-1)*multinomial(n, n-i*j, i$j), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);  # Alois P. Heinz, Mar 26 2024

Mathematica

nmax = 23; CoefficientList[Series[Product[1/(1 - x^k/k), {k, 2, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A007841, A371485, A371493.

Sequence in context: A025495 A028570 A009074 * A356868 A267344 A275132

Adjacent sequences: A371484 A371485 A371486 * A371488 A371489 A371490

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 25 2024

Status

approved