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
a(n) = [x^n] (1 + 4*x + 3*x^2 + x^3)^n. - Ilya Gutkovskiy, Apr 17 2025
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
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Apr 08 2011
STATUS
approved
