A108308 Expansion of 1/(1-x^2*c(2*x)), c(x) the g.f. of A000108.

1, 0, 1, 2, 9, 44, 245, 1462, 9157, 59368, 395033, 2682282, 18510561, 129451492, 915401757, 6534282398, 47020440413, 340733200288, 2484299720065, 18211441554706, 134145473550009, 992385470273692, 7370066147881413, 54927441150692742, 410673210445716085, 3079444191690216536

Offset

0,4

Comments

Diagonal sums of A110510.

Links

Table of n, a(n) for n=0..25.

Formula

a(0)=1, a(n) = Sum_{k=0..floor(n/2)} (k/(n-k))*C(2*n-3*k-1, n-2*k)*2^(n-2*k), n>0.

Conjecture: 2*(n-1)*a(n) + (41-17*n)*a(n-1) + 4*(2*n-5)*a(n-2) + (n-1)*a(n-3) + 4*(5-2*n)*a(n-4) = 0. - R. J. Mathar, Dec 10 2011

Prog

(PARI) my(x='x+O('x^30), c(x)=(1-sqrt(1-4*x))/(2*x)); Vec(1/(1-x^2*c(2*x))) \\ Michel Marcus, Oct 05 2025

Crossrefs

Cf. A000108, A110510.

Sequence in context: A371576 A246812 A365123 * A119855 A047119 A052881

Adjacent sequences: A108305 A108306 A108307 * A108309 A108310 A108311

Keyword

easy,nonn

Author

Paul Barry, Jul 24 2005

Extensions

More terms from Jason Yuen, Oct 05 2025

Status

approved