A381409 E.g.f. A(x) satisfies A(x) = exp( x * cos(x * A(x)^2) ).

1, 1, 1, -2, -59, -744, -6419, -6096, 1504553, 47199232, 911415481, 7309642880, -338340409043, -21607316073472, -725479564376475, -13094500078091264, 245361657851526353, 35579148236923486208, 1875350389057457406193, 57582879572195726819328

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• sign

Comments

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

Crossrefs

Cf. A185951, A381378.

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-2*k+1)^(k-1)*I^(n-k)*a185951(n, k));

Formula

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