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.

A187656 Convolution of the (signless) central Stirling numbers of the first kind (A187646).

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%I A187656 #13 May 28 2017 04:07:15
%S A187656 1,2,23,472,14109,557138,27417263,1617536576,111304630793,
%T A187656 8752522524930,774271257457719,76102169738598232,8227653697751043061,
%U A187656 970337814111625277394,123968202132756025685151,17055359730313188973301568
%N A187656 Convolution of the (signless) central Stirling numbers of the first kind (A187646).
%H A187656 G. C. Greubel, <a href="/A187656/b187656.txt">Table of n, a(n) for n = 0..250</a>
%F A187656 a(n) = Sum_{k=0..n} s(2*k,k)*s(2*n-2*k,n-k).
%F A187656 a(n) ~ n^n * c^(2*n) * 2^(3*n) / (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 A187656 seq(sum(abs(combinat[stirling1](2*k,k))*abs(combinat[stirling1](2*(n-k),n-k)),k=0..n),n=0..12);
%t A187656 Table[Sum[Abs[StirlingS1[2k, k]]Abs[StirlingS1[2n - 2k, n - k]], {k, 0, n}], {n, 0, 15}]
%o A187656 (Maxima) makelist(sum(abs(stirling1(2*k,k))*abs(stirling1(2*n-2*k,n-k)),k,0,n),n,0,12);
%o A187656 (PARI) a(n) = sum(k=0, n, abs(stirling(2*k, k, 1)*stirling(2*(n-k), n-k, 1))); \\ _Michel Marcus_, May 28 2017
%Y A187656 Cf. A187646.
%K A187656 nonn,easy
%O A187656 0,2
%A A187656 _Emanuele Munarini_, Mar 12 2011