cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A004996 a(n) = 6^n/n! * Product_{k=0..n-1} (6*k - 1).

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%I A004996 #19 Sep 08 2022 08:44:33
%S A004996 1,-6,-90,-1980,-50490,-1393524,-40412196,-1212365880,-37280250810,
%T A004996 -1168114525380,-37146041907084,-1195427166827976,-38851382921909220,
%U A004996 -1273129932671794440,-42013287778169216520
%N A004996 a(n) = 6^n/n! * Product_{k=0..n-1} (6*k - 1).
%H A004996 Seiichi Manyama, <a href="/A004996/b004996.txt">Table of n, a(n) for n = 0..500</a>
%F A004996 G.f.: (1 - 36*x)^(1/6).
%F A004996 a(n) ~ -1/6*Gamma(5/6)^-1*n^(-7/6)*6^(2*n)*{1 + 7/72*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
%F A004996 a(n) = 6^(2*n) * binomial(n-7/6, n). - _G. C. Greubel_, Aug 20 2019
%F A004996 D-finite with recurrence: n*a(n) +6*(-6*n+7)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020
%p A004996 seq(6^n*product(6*k-1, k = 0..n-1)/n!, n = 0..20); # _G. C. Greubel_, Aug 20 2019
%t A004996 Table[6^(2*n)*Pochhammer[-1/6, n]/n!, {n,0,20}] (* _G. C. Greubel_, Aug 20 2019 *)
%o A004996 (PARI) vector(20, n, n--; 6^n*prod(j=0,n-1, 6*j-1)/n! ) \\ _G. C. Greubel_, Aug 20 2019
%o A004996 (Magma) [1] cat [6^n*(&*[6*k-1: k in [0..n-1]])/Factorial(n): n in [1..20]]; // _G. C. Greubel_, Aug 20 2019
%o A004996 (Sage) [6^(2*n)*rising_factorial(-1/6, n)/factorial(n) for n in (0..20)] # _G. C. Greubel_, Aug 20 2019
%o A004996 (GAP) List([0..20], n-> 6^n*Product([0..n-1], k-> 6*k-1)/Factorial(n) ); # _G. C. Greubel_, Aug 20 2019
%Y A004996 Cf. A004993.
%K A004996 sign,easy
%O A004996 0,2
%A A004996 Joe Keane (jgk(AT)jgk.org)