A091541 - OEIS

%I #11 Sep 08 2022 08:45:13

%S 1,4,4,16,112,1120,14560,232960,4426240,97377280,2434432000,

%T 68164096000,2113086976000,71844957184000,2658263415808000,

%U 106330536632320000,4572213075189760000,210321801458728960000,10305768271477719040000

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

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

%H G. C. Greubel, <a href="/A091541/b091541.txt">Table of n, a(n) for n = 0..381</a>

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

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

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

%F 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

%t 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 *)

%o (PARI) x='x+O('x^50); Vec(serlaplace(3 - 2*(1 - 3*x)^(2/3))) \\ _G. C. Greubel_, Aug 15 2018

%o (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

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Feb 13 2004