A278689 a(n) = Sum_{k=0..n} binomial(n+k,n)*binomial(2*n-3,n-k-1) for n>1, a(n) = n for n<=1.

0, 1, 4, 25, 170, 1204, 8736, 64416, 480480, 3615040, 27382784, 208539136, 1595216896, 12247746560, 94330470400, 728474664960, 5638832087040, 43737154928640, 339856038297600, 2645063771750400, 20615846154731520, 160889637246074880, 1257082279931412480

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

Sequence in context: A175255 A081068 A163072 * A140177 A034494 A084210

Adjacent sequences: A278686 A278687 A278688 * A278690 A278691 A278692

Keyword

nonn

Author

Vladimir Kruchinin, Nov 26 2016

Status

approved