A381479 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)^2) ).

1, 1, 6, 69, 1200, 28085, 828240, 29502473, 1232606592, 59114482569, 3201204188160, 193215861134989, 12862437022076928, 936256855741871677, 73978404781917941760, 6306254322850544942865, 576881179288397985054720, 56369243043268551691136657, 5859726074013471622734938112

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(2*n+k+1,k)/(2*n+k+1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.

E.g.f.: ( (1/x) * Series_Reversion( x*(1 - x*cos(x))^2 ) )^(1/2).

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(2*n+k+1, k)/(2*n+k+1)*I^(n-k)*a185951(n, k));

Crossrefs

Cf. A185951, A364985, A381388.

Sequence in context: A235327 A381364 A349556 * A364982 A376123 A381175

Adjacent sequences: A381473 A381477 A381478 * A381480 A381485 A381486

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2025

Status

approved