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%I #25 Sep 08 2022 08:44:52
%S 1,21,546,15561,466830,14471730,458960580,14801478705,483514971030,
%T 15955994043990,530899438190940,17785131179396490,599222112044281740,
%U 20287948650642110340,689790254121831751560,23539092421907508521985
%N Related to sextic factorial numbers A008542.
%C Convolution of A004993(n-1) with A025751(n), n >= 1.
%H Michael De Vlieger, <a href="/A034789/b034789.txt">Table of n, a(n) for n = 1..645</a>
%H Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%F a(n) = 6^(n-1)*A008542(n)/n!.
%F G.f.: (-1+(1-36*x)^(-1/6))/6.
%F D-finite with recurrence: n*a(n) +6*(-6*n+5)*a(n-1)=0. - _R. J. Mathar_, Jan 28 2020
%p seq( 6^(n-1)*mul(6*j-5, j=1..n)/n!, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t Rest@ CoefficientList[Series[(-1 + (1 - 36 x)^(-1/6))/6, {x, 0, 16}], x] (* _Michael De Vlieger_, Oct 13 2019 *)
%t Table[6^(2*n-1)*Pochhammer[1/6, n]/n!, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o (PARI) vector(20, n, 6^(n-1)*prod(j=1,n, 6*j-5)/n! ) \\ _G. C. Greubel_, Nov 11 2019
%o (Magma) [6^(n-1)*(&*[6*j-5: j in [1..n]])/Factorial(n): n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o (Sage) [6^(n-1)*product( (6*j-5) for j in (1..n))/factorial(n) for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([1..20], n-> 6^(n-1)*Product([1..n], j-> 6*j-5)/Factorial(n) ); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A008542, A034687.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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