A091540 Rescaled second column A091539 of array A091534 ((5,2)-Stirling2).

1, 13, 184, 3040, 58360, 1283800, 31917760, 886123840, 27192323200, 914387689600, 33446228569600, 1322364153510400, 56203860301388800, 2555756347720576000, 123819357959385088000, 6367367706293321728000

Offset

2,2

Comments

A certain difference of two triple factorial sequences.

If offset 0: exponential (also called binomial) convolution of A091541 and A051606.

Links

G. C. Greubel, Table of n, a(n) for n = 2..380

Formula

a(n)= (5*2/fac3(3*n-1))*A091539(n), n>=2, with fac3(3*n-1) := A008544(n) (triple factorials).

E.g.f.: (1-2*x-(1-3*x)^(2/3))/(2*(1-3*x))= (1/2-x+int((1-3*x)^(-1/3), x))/(1-3*x).

E.g.f. with offset 0: (3-2*(1-3*x)^(2/3))/(1-3*x)^3.

a(n)=(fac3(3*n) - 3*fac3(3*n-2))/3! with fac3(3*n) := A032031(n)= n!*3^n and fac3(3*n-2) := A007559(n).

a(n) ~ 3^(n-1) * n! / 2. - Vaclav Kotesovec, Aug 16 2018

Mathematica

Drop[With[{nmax = 50}, CoefficientList[Series[(1 - 2*x - (1 - 3*x)^(2/3))/(2*(1 - 3*x)), {x, 0, nmax}], x]*Range[0, nmax]!], 2] (* G. C. Greubel, Aug 15 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace((1 - 2*x - (1 - 3*x)^(2/3))/(2*(1 - 3*x)))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (3-2*(1-3*x)^(2/3))/(1-3*x)^3 )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018

Crossrefs

Cf. A091541.

Sequence in context: A268413 A274345 A227503 * A057799 A057801 A377771

Adjacent sequences: A091537 A091538 A091539 * A091541 A091542 A091543

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 13 2004

Status

approved