A294467 Binomial transform of A088311.

1, 2, 5, 22, 113, 746, 6037, 55070, 548417, 6281938, 79935941, 1087584422, 16109401585, 255667890362, 4358283982613, 79893373511086, 1542859916102657, 31322024816838050, 676027617881188357, 15287136167625123638, 362322855217463741681

Offset

0,2

Links

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

Formula

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[Binomial[n, k]*k!*PartitionsQ[k], {k, 0, n}], {n, 0, 20}]

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(exp(x)*eta(x^2)/eta(x))) \\ G. C. Greubel, Oct 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x)*(&*[1 + x^k: k in [1..50]]))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 15 2018

Crossrefs

Cf. A266232, A294467, A294468.

Cf. A218481, A294466, A281425, A095051.

Sequence in context: A278439 A126797 A101206 * A177251 A041807 A228711

Adjacent sequences: A294464 A294465 A294466 * A294468 A294469 A294470

Keyword

nonn

Author

Vaclav Kotesovec, Oct 31 2017

Status

approved