A261186 a(n) = binomial(3*n-2,n+1).

4, 35, 252, 1716, 11440, 75582, 497420, 3268760, 21474180, 141120525, 927983760, 6107086800, 40225345056, 265182149218, 1749695026860, 11554258485616, 76360380541900, 505037289962205, 3342649210440540, 22138745874816900, 146721427591999680

Offset

2,1

Links

Table of n, a(n) for n=2..22.

Formula

G.f.: (3^(5/2) * cos(asin((3^(3/2) * sqrt(x))/2)/3) * x^(3/2))/(32*sin(asin((3^(3/2) * sqrt(x))/2)/3)^5 * sqrt(1-(27*x)/4)) - 1/x + 2.

+2*(n-2)*(2*n-3)*(n+1)*a(n) -3*(n-1)*(3*n-4)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Jun 07 2016

Mathematica

Table[Binomial[3 n - 2, n + 1], {n, 2, 25}] (* Vincenzo Librandi, Aug 12 2015 *)

Prog

(Maxima) taylor((3^(5/2)*cos(asin((3^(3/2)*sqrt(x))/2)/3)*x^(3/2))/(32*sin(asin((3^(3/2)*sqrt(x))/2)/3)^5*sqrt(1-(27*x)/4))-1/x+2, x, 0, 10);
(PARI) vector(30, n, n++; binomial(3*n-2, n+1)) \\ Michel Marcus, Aug 11 2015
(Magma) [Binomial(3*n-2, n+1): n in [2..30]]; // Vincenzo Librandi, Aug 12 2015

Crossrefs

Sequence in context: A128811 A220256 A220320 * A104526 A174436 A145607

Adjacent sequences: A261183 A261184 A261185 * A261187 A261188 A261189

Keyword

nonn

Author

Vladimir Kruchinin, Aug 11 2015

Status

approved