A381306 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^(1/2)) / A(x)^(1/2) ).

1, 1, 2, 5, 12, 1, -416, -5741, -60800, -543719, -3479424, 6260561, 822338048, 20933340065, 393396789248, 5840683299431, 54344509046784, -481407806103119, -44548560374988800, -1564969488082711811, -40856692743724335104, -812774967576805701599, -8614414458975040831488

Offset: 0

Author

Seiichi Manyama, Feb 19 2025

Keywords

• sign

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

Formula

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