A381518 - OEIS

A381518

Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + sin(x))^2 ) )^(1/2).

1, 1, 4, 29, 304, 4141, 68832, 1337881, 29432576, 712263961, 18403873280, 487814777141, 12296236382208, 230142147098501, -2906327530115072, -800177574047914831, -75835523291585773568, -6054072134316123116495, -459749417224473755910144, -34556942957229166465685555

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

Index entries for reversions of series

FORMULA

E.g.f. A(x) satisfies A(x) = 1 + sin(x*A(x)^2).

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

PROG

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