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 A381745 #20 Mar 06 2025 08:44:05
%S A381745 1,21,903,49525,3070308,204928371,14369906538,1043861319189,
%T A381745 77866470852108,5929621690613108,459076176165983247,
%U A381745 36026517938705145267,2859318461620989381900,229114879928544260792946,18509862380800289696106372,1506048000721264678984095445,123303480420582227597300406588
%N A381745 Expansion of exp( Sum_{k>=1} binomial(8*k-1,2*k) * x^k/k ).
%H A381745 Seiichi Manyama, <a href="/A381745/b381745.txt">Table of n, a(n) for n = 0..514</a>
%F A381745 G.f. A(x) satisfies A(x^2) = B(x)/x * B(-x)/(-x), where B(x) is the g.f. of A006632.
%F A381745 a(n) = Sum_{k=0..2*n} (-1)^k * A006632(k+1) * A006632(2*n-k+1).
%F A381745 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(8*k-1,2*k) * a(n-k).
%F A381745 G.f.: B(x)^3, where B(x) is the g.f. of A381751.
%o A381745 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(8*k-1, 2*k)*x^k/k)))
%Y A381745 Cf. A079489, A381744, A381746.
%Y A381745 Cf. A006632, A381751.
%K A381745 nonn,easy
%O A381745 0,2
%A A381745 _Seiichi Manyama_, Mar 05 2025