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A188686 Binomial transform of the sequence of binomial(3n,n). 9
1, 4, 22, 139, 934, 6484, 45931, 329893, 2393470, 17499892, 128732992, 951674398, 7064138779, 52616241370, 393052285291, 2943582912904, 22093111508686, 166141033332448, 1251528633163264, 9442096410241438, 71333250226656784 (list; graph; refs; listen; history; text; internal format)
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).

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.

Sequence in context: A142984 A283055 A097593 * A025756 A200731 A193116

Adjacent sequences:  A188683 A188684 A188685 * A188687 A188688 A188689

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Apr 08 2011

STATUS

approved

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Last modified September 23 15:06 EDT 2020. Contains 337310 sequences. (Running on oeis4.)