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 A381143 #9 Feb 15 2025 10:12:00
%S A381143 1,1,3,19,185,2381,38227,739271,16752465,435437209,12772234211,
%T A381143 417396070235,15040805940745,592531894182437,25336144876513395,
%U A381143 1168670193628654351,57845446906144852769,3058248577410499021361,172007282950136451003331,10255035157348348977955619
%N A381143 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * cosh(x)) ).
%C A381143 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381143 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381143 E.g.f. A(x) satisfies A(x) = exp( x * A(x) * cosh(x * A(x)) ).
%F A381143 a(n) = Sum_{k=0..n} (n+1)^(k-1) * A185951(n,k).
%o A381143 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381143 a(n) = sum(k=0, n, (n+1)^(k-1)*a185951(n, k));
%Y A381143 Cf. A003727, A162649, A381140.
%Y A381143 Cf. A185951.
%K A381143 nonn
%O A381143 0,3
%A A381143 _Seiichi Manyama_, Feb 15 2025