A381148 E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)) / A(x) ).

1, 1, 1, 0, -11, -88, -459, -560, 27945, 502336, 5223945, 18968576, -671465123, -20909349888, -345616002627, -2437013715968, 65881260463697, 3252353828442112, 76987773739473809, 873339053357432832, -17521718791602049595, -1354633521318944473088

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• sign

Crossrefs

Cf. A002017, A381142, A381145.

Cf. A136630, A185690.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (n-k+1)^(k-1)*I^(n-k)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} (n-k+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.