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A188918 Alternate partial sums of binomial(2n,n)*binomial(3n,n) (A006480). 2
1, 5, 85, 1595, 33055, 723701, 16429435, 382643525, 9082868245, 218790563255, 5332206228085, 131194789234955, 3253536973286245, 81224561099580155, 2039348104811147845, 51455631680563483835, 1303889832725451598495 (list; graph; refs; listen; history; text; internal format)
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: A012743 A139744 A195156 * A218139 A241330 A301435

Adjacent sequences:  A188915 A188916 A188917 * A188919 A188920 A188921

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Apr 14 2011

STATUS

approved

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Last modified March 20 19:52 EDT 2019. Contains 321349 sequences. (Running on oeis4.)