A381302 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^(1/2)) ).

1, 1, 2, 3, -12, -235, -2400, -18067, -51520, 1701009, 49829760, 872355319, 9861874176, -8805084275, -4518287900672, -159719520182055, -3608706518138880, -44358720138978463, 748112236681789440, 72503399560668659531, 2875934090148742430720, 73418478070342765464741

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..21.

Formula

a(n) = Sum_{k=0..n} k! * binomial(n/2+k/2+1,k)/(n/2+k/2+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/2+1, k)/(n/2+k/2+1)*I^(n-k)*a185951(n, k));

Crossrefs

Cf. A185951.

Sequence in context: A012713 A009814 A362289 * A345040 A196378 A336848

Adjacent sequences: A381299 A381300 A381301 * A381303 A381304 A381305

Keyword

sign

Author

Seiichi Manyama, Feb 19 2025

Status

approved