A358594 Expansion of e.g.f. Sum_{k>0} x^k / ((k-1)! - x^k).

1, 4, 9, 52, 125, 1626, 5047, 81768, 408249, 7263910, 39916811, 990191676, 6227020813, 174356750582, 1348633786515, 41861724727696, 355687428096017, 12904788209623614, 121645100408832019, 4866124222538035620, 51490090294307945301, 2248001455555300717294

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

a(n) = n! * Sum_{d|n} 1/(d-1)!^(n/d).

If p is prime, a(p) = p + p!.

Mathematica

a[n_] := n! * DivisorSum[n, 1/(#-1)!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/((k-1)!-x^k))))
(PARI) a(n) = n!*sumdiv(n, d, 1/(d-1)!^(n/d));

Crossrefs

Cf. A061095, A356668.

Sequence in context: A016489 A030694 A060998 * A370579 A368634 A009276

Adjacent sequences: A358591 A358592 A358593 * A358595 A358596 A358597

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2023

Status

approved