A385310 Expansion of e.g.f. 1/(1 - 2 * x * cos(x))^(1/2).

1, 1, 3, 12, 69, 500, 4455, 46928, 571977, 7914384, 122585355, 2100940864, 39470867469, 806555184448, 17808628411119, 422498774818560, 10717948285126545, 289501146405400832, 8295124400250875667, 251300745071590317056, 8025654235707259740885, 269482309052945201181696

Offset: 0

Author

Seiichi Manyama, Jun 24 2025

Keywords

• nonn

Crossrefs

Cf. A352252, A385311.

Cf. A380015, A385304, A385306, A385308.

Cf. A001147, A185951, A352646, A385283.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k)*I^(n-k)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} A001147(k) * i^(n-k) * A185951(n,k), where i is the imaginary unit and A185951(n,0) = 0^n.