A381182 E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sin(x * A(x)) ).

1, 1, 6, 71, 1288, 31661, 984640, 37085075, 1641305472, 83497838425, 4801347029504, 307975150996831, 21802395720298496, 1688562016007776261, 142023935786330431488, 12892154760586821775019, 1256251152910271399624704, 130793914073764385411654321, 14490427167940362294881615872

Offset: 0

Author

Seiichi Manyama, Feb 16 2025

Keywords

• nonn

Crossrefs

Cf. A201627, A381180, A381181.

Cf. A136630, A196776.

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

Formula

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