A034789 Related to sextic factorial numbers A008542.
1, 21, 546, 15561, 466830, 14471730, 458960580, 14801478705, 483514971030, 15955994043990, 530899438190940, 17785131179396490, 599222112044281740, 20287948650642110340, 689790254121831751560, 23539092421907508521985, 805867752326480585870310, 27668126163209166781547310
Offset: 1
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..645
- Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
- Index entries for sequences related to factorial numbers.
Programs
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GAP
List([1..20], n-> 6^(n-1)*Product([1..n], j-> 6*j-5)/Factorial(n) ); # G. C. Greubel, Nov 11 2019
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Magma
[6^(n-1)*(&*[6*j-5: j in [1..n]])/Factorial(n): n in [1..20]]; // G. C. Greubel, Nov 11 2019
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Maple
seq( 6^(n-1)*mul(6*j-5, j=1..n)/n!, n=1..20); # G. C. Greubel, Nov 11 2019
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Mathematica
Rest@ CoefficientList[Series[(-1 + (1 - 36 x)^(-1/6))/6, {x, 0, 16}], x] (* Michael De Vlieger, Oct 13 2019 *) Table[6^(2*n-1)*Pochhammer[1/6, n]/n!, {n, 20}] (* G. C. Greubel, Nov 11 2019 *) -
PARI
vector(20, n, 6^(n-1)*prod(j=1,n, 6*j-5)/n! ) \\ G. C. Greubel, Nov 11 2019
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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
Formula
a(n) = 6^(n-1)*A008542(n)/n!.
G.f.: (-1+(1-36*x)^(-1/6))/6.
D-finite with recurrence: n*a(n) + 6*(-6*n+5)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
a(n) ~ 6^(2*n-1) * n^(-5/6) / Gamma(1/6). - Amiram Eldar, Aug 18 2025
Comments