cp's OEIS Frontend

A034789 Related to sextic factorial numbers A008542.

%I A034789 #32 Aug 18 2025 02:12:15
%S A034789 1,21,546,15561,466830,14471730,458960580,14801478705,483514971030,
%T A034789 15955994043990,530899438190940,17785131179396490,599222112044281740,
%U A034789 20287948650642110340,689790254121831751560,23539092421907508521985,805867752326480585870310,27668126163209166781547310
%N A034789 Related to sextic factorial numbers A008542.
%C A034789 Convolution of A004993(n-1) with A025751(n), n >= 1.
%H A034789 Michael De Vlieger, <a href="/A034789/b034789.txt">Table of n, a(n) for n = 1..645</a>
%H A034789 Elżbieta Liszewska and Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H A034789 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A034789 a(n) = 6^(n-1)*A008542(n)/n!.
%F A034789 G.f.: (-1+(1-36*x)^(-1/6))/6.
%F A034789 D-finite with recurrence: n*a(n) + 6*(-6*n+5)*a(n-1) = 0. - _R. J. Mathar_, Jan 28 2020
%F A034789 a(n) ~ 6^(2*n-1) * n^(-5/6) / Gamma(1/6). - _Amiram Eldar_, Aug 18 2025
%p A034789 seq( 6^(n-1)*mul(6*j-5, j=1..n)/n!, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t A034789 Rest@ CoefficientList[Series[(-1 + (1 - 36 x)^(-1/6))/6, {x, 0, 16}], x] (* _Michael De Vlieger_, Oct 13 2019 *)
%t A034789 Table[6^(2*n-1)*Pochhammer[1/6, n]/n!, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o A034789 (PARI) vector(20, n, 6^(n-1)*prod(j=1,n, 6*j-5)/n! ) \\ _G. C. Greubel_, Nov 11 2019
%o A034789 (Magma) [6^(n-1)*(&*[6*j-5: j in [1..n]])/Factorial(n): n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o A034789 (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 A034789 (GAP) List([1..20], n-> 6^(n-1)*Product([1..n], j-> 6*j-5)/Factorial(n) ); # _G. C. Greubel_, Nov 11 2019
%Y A034789 Cf. A004993, A008542, A025751, A034687, A175379.
%K A034789 easy,nonn
%O A034789 1,2
%A A034789 _Wolfdieter Lang_