A381384 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) / A(x)^2 ).

1, 1, 2, 5, 0, -299, -5840, -90791, -1210496, -11174519, 71397888, 8367496301, 327020705792, 9709296136541, 226223975684096, 2946493117173761, -87437164233621504, -9675847870039338095, -535455805780063748096, -22518479178045130002731, -706013052362778282033152

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• sign

Crossrefs

Cf. A364980, A381376, A381378, A381382.

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(2*n-k+1, k)/(2*n-k+1)*I^(n-k)*a136630(n, k));

Formula

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