A294468 Inverse binomial transform of A088311.

1, 0, 1, 8, 9, 224, 1225, 11304, 103537, 1431296, 15642801, 206721800, 3295533241, 47467875168, 859354139449, 15596241280424, 283240963555425, 5859309797252864, 129874369387025377, 2752905169704533256, 67640333903657850601

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..443

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A088311(k).

a(n) ~ exp(-1) * n! * A000009(n).

a(n) ~ sqrt(2*Pi) * exp(Pi*sqrt(n/3) - n - 1) * n^(n - 1/4) / (4*3^(1/4)).

E.g.f.: exp(-x) * Product_{k>=1} (1 + x^k). - Ilya Gutkovskiy, Oct 15 2018

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[n, k]*k!*PartitionsQ[k], {k, 0, n}], {n, 0, 20}]
max = 20; t = Table[k!*PartitionsQ[k], {k, 0, max}]; Table[Differences[t, n], {n, 0, max}][[All, 1]] (* Jean-François Alcover, Nov 02 2017 *)

Crossrefs

Cf. A266232, A294467, A293467.

Cf. A218481, A294466, A281425, A095051.

Sequence in context: A041142 A307947 A175849 * A041605 A239524 A115073

Adjacent sequences: A294465 A294466 A294467 * A294469 A294470 A294471

Keyword

nonn

Author

Vaclav Kotesovec, Oct 31 2017

Status

approved