A380271 Denominators of coefficients in expansion of exp(-1 + 1 / Product_{k>=1} (1 - x^k)).

1, 1, 2, 6, 24, 120, 720, 1008, 40320, 72576, 3628800, 39916800, 95800320, 6227020800, 3487131648, 1307674368000, 20922789888000, 2845499424768, 6402373705728000, 24329020081766400, 187146308321280000, 51090942171709440000, 224800145555521536000, 25852016738884976640000

Offset

0,3

Links

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

Formula

b(0) = 1, b(n) = (1/n) * Sum_{k=1..n} k * A000041(k) * b(n-k), a(n) = denominator of b(n).

Example

1, 1, 5/2, 31/6, 265/24, 2621/120, 31621/720, 85319/1008, 6574961/40320, ...

Mathematica

nmax = 23; CoefficientList[Series[Exp[-1 + 1/Product[1 - x^k, {k, 1, nmax}]], {x, 0, nmax}], x] // Denominator
b[0] = 1; b[n_] := b[n] = (1/n) Sum[k PartitionsP[k] b[n - k], {k, 1, n}]; a[n_] := Denominator[b[n]]; Table[a[n], {n, 0, 23}]

Crossrefs

Cf. A000041, A017666, A058892, A066186, A067653, A098988, A380171 (numerators).

Sequence in context: A319546 A232983 A319207 * A263749 A329498 A000805

Adjacent sequences: A380267 A380268 A380269 * A380272 A380273 A380274

Keyword

nonn,frac,new

Author

Ilya Gutkovskiy, Jan 18 2025

Status

approved