A381745 - OEIS

%I #20 Mar 06 2025 08:44:05

%S 1,21,903,49525,3070308,204928371,14369906538,1043861319189,

%T 77866470852108,5929621690613108,459076176165983247,

%U 36026517938705145267,2859318461620989381900,229114879928544260792946,18509862380800289696106372,1506048000721264678984095445,123303480420582227597300406588

%N Expansion of exp( Sum_{k>=1} binomial(8*k-1,2*k) * x^k/k ).

%H Seiichi Manyama, <a href="/A381745/b381745.txt">Table of n, a(n) for n = 0..514</a>

%F G.f. A(x) satisfies A(x^2) = B(x)/x * B(-x)/(-x), where B(x) is the g.f. of A006632.

%F a(n) = Sum_{k=0..2*n} (-1)^k * A006632(k+1) * A006632(2*n-k+1).

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(8*k-1,2*k) * a(n-k).

%F G.f.: B(x)^3, where B(x) is the g.f. of A381751.

%o (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 Cf. A079489, A381744, A381746.

%Y Cf. A006632, A381751.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Mar 05 2025