A381176 E.g.f. A(x) satisfies A(x) = 1 + x*cos(x*A(x)).

1, 1, 0, -3, -24, -55, 480, 8813, 61824, -264591, -13662720, -185252771, -117427200, 52162650553, 1214778679296, 7998339208845, -370278535495680, -14623177924271263, -202753399336206336, 3863010744775239101, 286065782789626920960, 6603193175290504771881

Offset: 0

Author

Seiichi Manyama, Feb 16 2025

Keywords

• sign

Comments

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

Crossrefs

Cf. A381173, A381174, A381175.

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

Formula

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