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 A381171 #13 Feb 16 2025 09:41:01
%S A381171 1,1,2,9,72,725,8640,124117,2117248,41477193,913305600,22371549761,
%T A381171 604476094464,17858943664861,572524035586048,19793963392789965,
%U A381171 734249332747960320,29090332675789113617,1225991945551031304192,54765451909152748484857,2584803582762012599910400
%N A381171 Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cosh(x)) ).
%C A381171 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381171 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381171 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)) ).
%F A381171 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(n+1,k) * A185951(n,k).
%o A381171 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381171 a(n) = sum(k=0, n, k!*binomial(n+1, k)*a185951(n, k))/(n+1);
%Y A381171 Cf. A162654, A215364, A381172.
%Y A381171 Cf. A162653, A381173, A381181.
%Y A381171 Cf. A185951.
%K A381171 nonn
%O A381171 0,3
%A A381171 _Seiichi Manyama_, Feb 16 2025