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.

A376387 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + x*log(1-x))^3 ) )^(2/3).

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%I A376387 #13 Sep 22 2024 11:15:14
%S A376387 1,0,4,6,376,2220,125028,1614480,92285856,2018520000,121850616240,
%T A376387 3907998135360,253836993367296,10891474747433280,768302761361304960,
%U A376387 41447634607068318720,3187906294983450762240,206982374312337802536960,17368877655215923728595968
%N A376387 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + x*log(1-x))^3 ) )^(2/3).
%H A376387 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A376387 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371232.
%F A376387 a(n) = (2 * n!/(3*n+2)!) * Sum_{k=0..floor(n/2)} (3*n+k+1)! * |Stirling1(n-k,k)|/(n-k)!.
%o A376387 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+x*log(1-x))^3)/x)^(2/3)))
%o A376387 (PARI) a(n) = 2*n!*sum(k=0, n\2, (3*n+k+1)!*abs(stirling(n-k, k, 1))/(n-k)!)/(3*n+2)!;
%Y A376387 Cf. A371232, A376386.
%K A376387 nonn
%O A376387 0,3
%A A376387 _Seiichi Manyama_, Sep 22 2024