OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (sqrt(1-8*x)*(2*x-1)+10*x+1)/(16*sqrt(1-8*x)).
a(n) ~ 9*8^(n-2)/sqrt(Pi*n). - Ilya Gutkovskiy, Nov 26 2016
MAPLE
a:= proc(n) option remember; `if`(n<3, n^2,
(9*n-2)*(8*n-12)*a(n-1)/((9*n-11)*n))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 26 2016
MATHEMATICA
CoefficientList[Series[(Sqrt[1 - 8 x] (2 x - 1) + 10 x + 1) / (16 Sqrt[1 - 8 x]), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 26 2016 *)
a[n_] := Binomial[2n-3, n-1] Hypergeometric2F1[1-n, n+1, n-1, -1]; a[0]=0;
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 03 2017 *)
PROG
(Maxima)
taylor((sqrt(1-8*x)*(2*x-1)+10*x+1)/(16*sqrt(1-8*x)), x, 0, 10);
a(n):=sum(binomial(n+k, n)*binomial(2*n-3, n-k-1), k, 0, n);
(PARI) a(n)=sum(k=0, n, binomial(n+k, n)*binomial(2*n-3, n-k-1)) \\ Michel Marcus, Nov 27 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Nov 26 2016
STATUS
approved