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A154623 Sequence with g.f. 1+(x/(1-5*x))*c(x/(1-5*x)), c(x) the g.f. of A000108. 3
1, 1, 6, 37, 235, 1539, 10392, 72267, 516474, 3783115, 28317562, 215969271, 1673702191, 13148444197, 104494340880, 838670818365, 6788255966595, 55346471893395, 454123503938490, 3746885525588175, 31066887028255065 (list; graph; refs; listen; history; text; internal format)
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: A317629 A081912 A081188 * A196834 A005389 A080954

Adjacent sequences:  A154620 A154621 A154622 * A154624 A154625 A154626

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 13 2009

STATUS

approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)