A188686 Binomial transform of the sequence of binomial(3n,n).

1, 4, 22, 139, 934, 6484, 45931, 329893, 2393470, 17499892, 128732992, 951674398, 7064138779, 52616241370, 393052285291, 2943582912904, 22093111508686, 166141033332448, 1251528633163264, 9442096410241438, 71333250226656784

Offset

0,2

Comments

Binomial transform of A005809.

Links

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

Formula

G.f.: 2*cos((1/3)*arcsin(3/2*sqrt(3x/(1-x))))/sqrt(4-35x+31x^2).

D-finite recurrence: 2*n*(2*n-1)*a(n) = (39*n^2-43*n+12)*a(n-1) - 2*(n-1)*(33*n-34)*a(n-2) + 31*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 31^(n+1/2)/(6*4^n*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 20 2012

Mathematica

Table[Sum[Binomial[n, k]Binomial[3k, k], {k, 0, n}], {n, 0, 22}]

Prog

(Maxima) makelist(sum(binomial(n, k)*binomial(3*k, k), k, 0, n), n, 0, 20);

Crossrefs

Cf. A005809, A359643.

Sequence in context: A142984 A283055 A097593 * A025756 A366119 A200731

Adjacent sequences: A188683 A188684 A188685 * A188687 A188688 A188689

Keyword

nonn,easy

Author

Emanuele Munarini, Apr 08 2011

Status

approved