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.

A346767 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(6*k,k) / (5*k + 1).

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%I A346767 #11 Aug 02 2021 17:38:34
%S A346767 1,1,7,70,855,11907,182714,3029040,53565875,1001599339,19674910572,
%T A346767 404009742858,8638256718929,191702754433132,4403979321915615,
%U A346767 104496256532120370,2555972287817569101,64340126437548435175,1664318438781195696512,44182488823505663971205
%N A346767 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(6*k,k) / (5*k + 1).
%C A346767 Stirling transform of A002295.
%H A346767 Michael De Vlieger, <a href="/A346767/b346767.txt">Table of n, a(n) for n = 0..499</a>
%F A346767 G.f.: Sum_{k>=0} ( binomial(6*k,k) / (5*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).
%t A346767 Table[Sum[StirlingS2[n, k] Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 19}]
%t A346767 nmax = 19; CoefficientList[Series[Sum[(Binomial[6 k, k]/(5 k + 1)) x^k/Product[1 - j x, {j, 0, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%t A346767 nmax = 19; CoefficientList[Series[HypergeometricPFQ[{1/6, 1/3, 1/2, 2/3, 5/6}, {2/5, 3/5, 4/5, 1, 6/5}, 46656 (Exp[x] - 1)/3125], {x, 0, nmax}], x] Range[0, nmax]!
%o A346767 (PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(6*k, k)/(5*k + 1)); \\ _Michel Marcus_, Aug 02 2021
%Y A346767 Cf. A002295, A064856, A346764, A346765, A346766, A346768, A346769.
%K A346767 nonn
%O A346767 0,3
%A A346767 _Ilya Gutkovskiy_, Aug 02 2021