A381417 E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^2) ).

1, 1, 5, 48, 693, 13432, 327561, 9639224, 332476361, 13157303104, 587704852749, 29250533304960, 1605304225302525, 96313936238637184, 6271774683977444817, 440545491471769836032, 33204015428071302059025, 2672942015998405569765376, 228892490007003118401996565

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Crossrefs

Cf. A136630.

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, (2*n+1)^(k-1)*I^(n-k)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.