A381175 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)) ).

1, 1, 6, 69, 1224, 29465, 898320, 33187133, 1441200768, 71956238769, 4061414246400, 255737764687669, 17773804761259008, 1351494159065894857, 111608708333568036864, 9947544079380663728685, 951770403836914402099200, 97301151510219112917218657, 10585077723403580668983902208

Offset

0,3

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} k! * binomial(n+2*k+1,k)/(n+2*k+1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.

Prog

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

Crossrefs

Cf. A381173, A381174, A381176.

Cf. A364984, A381172.

Cf. A185951.

Sequence in context: A381479 A364982 A376123 * A098639 A305110 A235328

Adjacent sequences: A381172 A381173 A381174 * A381176 A381177 A381178

Keyword

nonn

Author

Seiichi Manyama, Feb 16 2025

Status

approved