A152297 Alternate binomial partial sums of binomial(2n,n)*binomial(3n,n) (A006480).

1, 5, 79, 1427, 28447, 599435, 13100065, 293737085, 6713171455, 155700711995, 3653740285729, 86561367835805, 2067026079739921, 49689509437820933, 1201321507453119103, 29187308928225658787, 712192597620218620735

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = sum((-1)^(n-k)*binomial(n,k)*binomial(2*k,k)*binomial(3*k,k),k=0..n).

D-finite with recurrence Recurrence: (n+3)^2*a(n+3)-(24*n^2+120*n+149)*a(n+2)-51*(n+2)^2*a(n+1)-26*(n+1)*(n+2)*a(n)=0.

E.g.f.: exp(-x)*F(1/3,2/3;1,1;27*x), where F(a1,a2;b1;z) is a hypergeometric series.

a(n) ~ 13*sqrt(3) * 26^n / (27*Pi*n). - Vaclav Kotesovec, Mar 02 2014

Mathematica

Table[Sum[Binomial[n, k]Binomial[2k, k]Binomial[3k, k](-1)^(n-k), {k, 0, n}], {n, 0, 16}]

Prog

(Maxima) makelist(sum((-1)^(n-k)*binomial(n, k)*binomial(2*k, k)*binomial(3*k, k), k, 0, n), n, 0, 16);

Crossrefs

Cf. A006480, A188441, A188918, A188946.

Sequence in context: A197747 A198152 A197232 * A366640 A244585 A293786

Adjacent sequences: A152294 A152295 A152296 * A152298 A152299 A152300

Keyword

nonn,easy

Author

Emanuele Munarini, Apr 14 2011

Status

approved