A381389 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) )^2.

1, 2, 14, 178, 3344, 83722, 2628000, 99358810, 4398573568, 223280915090, 12788876882176, 816044058415298, 57411735641690112, 4415467258014111002, 368568207039291072512, 33186631279383615035242, 3206409506796711229521920, 330893672854541429428877602

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381388.

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381388.

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

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