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A091541 Four times triple factorials (3*n-2)!!! with leading 1 added. 2
1, 4, 4, 16, 112, 1120, 14560, 232960, 4426240, 97377280, 2434432000, 68164096000, 2113086976000, 71844957184000, 2658263415808000, 106330536632320000, 4572213075189760000, 210321801458728960000, 10305768271477719040000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)