A381305 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^(1/2)) / A(x)^(3/2) ).

1, 1, 0, -1, -4, 1, 32, 181, -192, -4919, -31616, 88571, 2089984, 13830545, -83841024, -1884928471, -11874992128, 142704083281, 3085703610368, 16806597846295, -397246640947200, -8257973126103359, -32717082633175040, 1686557057210338589, 33490001971564773376

Offset: 0

Author

Seiichi Manyama, Feb 19 2025

Keywords

• sign

Crossrefs

Cf. A136630.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(n/2-k/2+1, k)/(n/2-k/2+1)*I^(n-k)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(n/2-k/2+1,k)/(n/2-k/2+1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.