A381342 Expansion of e.g.f. exp( x * cos(sqrt(2)*x) ).

1, 1, 1, -5, -23, -39, 361, 2675, 3697, -90575, -741839, 52779, 48483865, 358510985, -1225182503, -43006420829, -239523048095, 2745896185953, 54532102774753, 144304368441179, -6547928921714999, -88336890555248327, 199686588300036553, 18186115601328322515

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. A003727, A009189, A381273, A381274, A381275, A381276, A381341.

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, (-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-1,2*k) * a(n-2*k-1).

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