A381345 Expansion of e.g.f. 1/( 1 - x * cos(sqrt(2)*x) ).

1, 1, 2, 0, -24, -220, -1200, -2576, 52864, 1016208, 10909440, 57039488, -687971328, -26190716864, -450123634688, -4238375059200, 24514848522240, 2156422420074752, 54984136073084928, 799573460292407296, 42320889956270080, -425007017470737816576, -15563879892284330213376

Offset: 0

Author

Seiichi Manyama, Feb 20 2025

Keywords

• sign

Comments

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

Crossrefs

Cf. A205571, A352252, A381280, A381281, A381282, A381283, A381344.

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)^((n-k)/2)*a185951(n, k));

Formula

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

a(n) = Sum_{k=0..n} k! * (-2)^((n-k)/2) * A185951(n,k).