A381388 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) ).

1, 1, 6, 71, 1280, 31201, 961184, 35838991, 1569696768, 79007365921, 4494170889472, 285130996517399, 19963494971809792, 1529055924661457921, 127179971644212387840, 11416028319985437309215, 1099976414821996358795264, 113239907265894992879189185, 12404749306625020735299780608

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381389.

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

Formula

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

E.g.f.: ( (1/x) * Series_Reversion( x*(1 - sin(x))^2 ) )^(1/2).