A381378 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^2) ).

1, 1, 2, 3, -48, -1135, -18240, -231637, -1356544, 53849889, 3026119680, 100808786419, 2429052865536, 26284690243825, -1539261873164288, -140633348417624805, -7196339681250508800, -258335768147494234303, -4225401456668904259584, 307227604973975435785571

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• sign

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A364980, A381376, A381382, A381384.

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(2*n-k+1, k)/(2*n-k+1)*I^(n-k)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(2*n-k+1,k)/(2*n-k+1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.