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.
%I A381443 #13 Feb 24 2025 08:52:31
%S A381443 1,3,24,333,6720,179523,5992800,240498261,11287790592,607019415075,
%T A381443 36813049552896,2486167829854173,185070328813031424,
%U A381443 15056826823777670883,1329283990371617820672,126573877370649849898149,12930948581449447912243200,1410875453109072905123881923
%N A381443 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sinh(x))^3 ).
%H A381443 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381443 E.g.f. A(x) satisfies A(x) = (1 + sinh(x*A(x)))^3.
%F A381443 E.g.f.: B(x)^3, where B(x) is the e.g.f. of A381430.
%F A381443 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(3*n+3,k) * A136630(n,k).
%o A381443 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381443 a(n) = sum(k=0, n, k!*binomial(3*n+3, k)*a136630(n, k))/(n+1);
%Y A381443 Cf. A377554, A381450.
%Y A381443 Cf. A136630, A381430.
%K A381443 nonn
%O A381443 0,2
%A A381443 _Seiichi Manyama_, Feb 23 2025