A188918 Alternate partial sums of binomial(2n,n)*binomial(3n,n) (A006480).

1, 5, 85, 1595, 33055, 723701, 16429435, 382643525, 9082868245, 218790563255, 5332206228085, 131194789234955, 3253536973286245, 81224561099580155, 2039348104811147845, 51455631680563483835, 1303889832725451598495

Offset

0,2

Links

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

Formula

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

Recurrence: (n+2)^2*a(n+2)-(26*n^2+77*n+56)*a(n+1)-3*(9*n^2+27*n+20)*a(n)=0.

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

a(n) ~ 3^(3*n + 7/2) / (56*Pi*n). - Vaclav Kotesovec, Nov 27 2017

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[2k, k]Binomial[3k, k], {k, 0, n}], {n, 0, 16}] (* fixed by Vaclav Kotesovec, Nov 27 2017 *)

Prog

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

Crossrefs

Cf. A006480, A188441, A188946, A152297.

Sequence in context: A359234 A139744 A195156 * A349936 A218139 A241330

Adjacent sequences: A188915 A188916 A188917 * A188919 A188920 A188921

Keyword

nonn,easy

Author

Emanuele Munarini, Apr 14 2011

Status

approved