A354478 a(n) is the numerator of Sum_{k=1..n} 1 / Stirling1(n,k).

1, 0, 7, 25, 3991, 3923773, 4901627, 527165212865, 9823031039961293027, 123877274974851473572937, 443645907754951021537851199, 246932542361393897304051461727006396307, 1474846779473982897350113519971401527250089, 46578509609937575127608478711343978511593638945099881

Offset

1,3

Comments

Conjecture: a(n)/A354479(n) tends to 1 as n tends to infinity. For comparison: A112290(n)/A112291(n) tends to 2 as n tends to infinity. - Vaclav Kotesovec, Jun 02 2022

Links

Table of n, a(n) for n=1..14.

Example

1, 0, 7/6, 25/33, 3991/4200, 3923773/4192200, 4901627/5115600, 527165212865/545250747888, ...

Mathematica

Table[Sum[1/StirlingS1[n, k], {k, 1, n}], {n, 1, 14}] // Numerator

Prog

(PARI) a(n) = numerator(sum(k=1, n, 1/stirling(n, k, 1))); \\ Michel Marcus, Jun 02 2022

Crossrefs

Cf. A008275, A046825, A112288, A112290, A354479 (denominators).

Sequence in context: A342584 A335498 A012490 * A157702 A063453 A284054

Adjacent sequences: A354475 A354476 A354477 * A354479 A354480 A354481

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Jun 02 2022

Status

approved