A154623 Sequence with g.f. 1+(x/(1-5*x))*c(x/(1-5*x)), c(x) the g.f. of A000108.

1, 1, 6, 37, 235, 1539, 10392, 72267, 516474, 3783115, 28317562, 215969271, 1673702191, 13148444197, 104494340880, 838670818365, 6788255966595, 55346471893395, 454123503938490, 3746885525588175, 31066887028255065

Offset

0,3

Comments

Hankel transform is F(4n+1) (A033889).

a(n+1) is the 5th binomial transform of A000108.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f.: (1/2)*(3-sqrt((1-9*x)/(1-5*x))).

a(n)=(4/5)*0^n+sum{k=0..n-1, C(n-1,k)*A000108(k)*5^(n-k-1)}.

Conjecture: n*a(n) +2*(8-7n)*a(n-1) +45*(n-2)*a(n-2) = 0. - R. J. Mathar, Dec 14 2011

a(n) ~ 3^(2*n+1)/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012

a(n) = (-1)^(n-1)*(GegenbauerC(n-1,-n+1,7/2) + GegenbauerC(n-2,-n+1,7/2)) for n>=1. - Peter Luschny, May 13 2016

Mathematica

CoefficientList[Series[1/2*(3-Sqrt[(1-9*x)/(1-5*x)]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

Crossrefs

Sequence in context: A081912 A081188 A218186 * A196834 A005389 A080954

Adjacent sequences: A154620 A154621 A154622 * A154624 A154625 A154626

Keyword

easy,nonn

Author

Paul Barry, Jan 13 2009

Status

approved