A091541 Four times triple factorials (3*n-2)!!! with leading 1 added.

1, 4, 4, 16, 112, 1120, 14560, 232960, 4426240, 97377280, 2434432000, 68164096000, 2113086976000, 71844957184000, 2658263415808000, 106330536632320000, 4572213075189760000, 210321801458728960000, 10305768271477719040000

Offset

0,2

Comments

The exponential (or binomial) convolution of a(n) with A051606(n) gives A091540.

Links

G. C. Greubel, Table of n, a(n) for n = 0..381

Formula

a(0)=1, a(n)=4*(3*n-2)!!! = 4*A007559(n-1), n>=1.

E.g.f. 3-2*(1-3*x)^(2/3).

E.g.f. for a(n+1)/4 = A007559(n), n>=0: (1-3*x)^(-1/3).

G.f.: 3-G(0), where G(k)= 1 + 1/(1 - x*(3*k-2)/(x*(3*k-2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 11 2013

Mathematica

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

Prog

(PARI) x='x+O('x^50); Vec(serlaplace(3 - 2*(1 - 3*x)^(2/3))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(3 - 2*(1 - 3*x)^(2/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018

Crossrefs

Sequence in context: A075225 A204078 A284494 * A094354 A263389 A019062

Adjacent sequences: A091538 A091539 A091540 * A091542 A091543 A091544

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 13 2004

Status

approved