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.

A187659 Convolution of the (signless) central Stirling numbers of the first kind (A187646) and the central Stirling numbers of the second kind (A007820).

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%I A187659 #13 May 28 2017 04:07:31
%S A187659 1,2,19,333,8862,322885,15061381,858280605,57766424400,4479377168841,
%T A187659 392785285842806,38393983653735732,4136603248470746422,
%U A187659 486806030644218961182,62109988002922704031388,8537900524822110186179616
%N A187659 Convolution of the (signless) central Stirling numbers of the first kind (A187646) and the central Stirling numbers of the second kind (A007820).
%H A187659 G. C. Greubel, <a href="/A187659/b187659.txt">Table of n, a(n) for n = 0..250</a>
%F A187659 a(n) = Sum_{k=0..n} s(2*k,k)*S(2*n-2*k,n-k).
%F A187659 a(n) ~ n^n * c^(2*n) * 2^(3*n-1) / (sqrt(Pi*(c-1)*n) * exp(n) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2). - _Vaclav Kotesovec_, May 21 2014
%p A187659 seq(sum(abs(combinat[stirling1](2*k,k))*combinat[stirling2](2*(n-k),n-k),k=0..n),n=0..12);
%t A187659 Table[Sum[Abs[StirlingS1[2k, k]]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 15}]
%o A187659 (Maxima) makelist(sum(abs(stirling1(2*k,k))*stirling2(2*n-2*k,n-k),k,0,n),n,0,12);
%o A187659 (PARI) a(n) = sum(k=0, n, abs(stirling(2*k, k, 1)*stirling(2*(n-k), n-k, 2))); \\ _Michel Marcus_, May 28 2017
%Y A187659 Cf. A007820, A187646.
%K A187659 nonn,easy
%O A187659 0,2
%A A187659 _Emanuele Munarini_, Mar 12 2011