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 A381521 #11 Feb 26 2025 06:26:36
%S A381521 1,2,10,78,792,9250,106080,636286,-30646784,-2237508990,-112000654080,
%T A381521 -5124930562642,-227068649702400,-9819508698442846,
%U A381521 -406371251899045888,-15094508095346343330,-394372545425757634560,7096803535075158290434,2430273114806112504446976
%N A381521 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cos(x))^2 ).
%C A381521 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381521 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381521 E.g.f. A(x) satisfies A(x) = (1 + x*A(x) * cos(x*A(x)))^2.
%F A381521 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381520.
%F A381521 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(2*n+2,k) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381521 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381521 a(n) = sum(k=0, n, k!*binomial(2*n+2, k)*I^(n-k)*a185951(n, k))/(n+1);
%Y A381521 Cf. A185951, A381480, A381520.
%Y A381521 Cf. A377553, A381442, A381449, A381519.
%K A381521 sign
%O A381521 0,2
%A A381521 _Seiichi Manyama_, Feb 26 2025