A110508 Expansion of 1/(1-(x+x^2)c(2x)), c(x) the g.f. of A000108.

1, 1, 4, 17, 87, 490, 2945, 18517, 120340, 802005, 5451651, 37652546, 263480357, 1864065017, 13311094644, 95816113129, 694511157535, 5064818563258, 37135165923801, 273581694291309, 2024194855052180, 15034769479254861

Offset

0,3

Comments

Diagonal sums of A110506.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms n=0..200 from Vincenzo Librandi)

Formula

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

Conjecture: n*(3*n-7)*a(n) -4*(3*n-4)*(2*n-5)*a(n-1) +2*n*(3*n-7) +(-45*n^2+177*n-160)*a(n-3) -4*(3*n-4)*(2*n-5)*a(n-4) = 0. - R. J. Mathar, Nov 15 2011

a(n) ~ 9 * 2^(3*n+4) / (529 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 08 2014

Mathematica

CoefficientList[Series[1/(1-(x+x^2)*(1-Sqrt[1-8*x])/(4*x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 08 2014 *)

Prog

(PARI) x='x+O('x^50); Vec(1/(1-(x+x^2)*(1-sqrt(1-8*x))/(4*x))) \\ G. C. Greubel, Aug 29 2017

Crossrefs

Sequence in context: A321384 A056542 A331158 * A114190 A135168 A364212

Adjacent sequences: A110505 A110506 A110507 * A110509 A110510 A110511

Keyword

nonn,easy

Author

Paul Barry, Jul 24 2005

Status

approved