A381282 Expansion of e.g.f. 1/(1 - x * cos(2*x)).

1, 1, 2, -6, -72, -520, -1200, 24752, 516992, 5106816, 5287680, -998945024, -23719719936, -272471972864, 1326261594112, 149170761246720, 3843177252618240, 42752553478356992, -863092250325614592, -59317347865870139392, -1577115871098630307840, -13173264127625587851264

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• sign

Comments

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

Crossrefs

Cf. A352252, A381283.

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!*(2*I)^(n-k)*a185951(n, k));

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-4)^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).

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