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A188676 Alternate partial sums of the binomial coefficients binomial(3*n,n). 11
1, 2, 13, 71, 424, 2579, 15985, 100295, 635176, 4051649, 25993366, 167543354, 1084134346, 7038291098, 45821937982, 299045487602, 1955803426045, 12815265660680, 84111082917925, 552872886403775, 3638971619401720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

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

Recurrence: 2*(n+2)*(2n+3)*a(n+2)-(23*n^2+67*n+48)*a(n+1)-3*(3*n+4)*(3n+5)*a(n)=0.

G.f.: 2*cos((1/3)*arcsin(3*sqrt(3*x)/2))/((1+x)*sqrt(4-27*x)).

a(n) ~ 3^(3*n+7/2)/(62*4^n*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 20 2012

MATHEMATICA

Table[Sum[Binomial[3k, k](-1)^(n-k), {k, 0, n}], {n, 0, 20}]

PROG

(Maxima) makelist(sum(binomial(3*k, k)*(-1)^(n-k), k, 0, n), n, 0, 20);

CROSSREFS

Cf. A005809, A001764, A104859, A188678, A188679, A188680, A188681, A188682, A188683, A188684, A188685, A188686, A188687.

Sequence in context: A218184 A264735 A289926 * A097349 A289790 A109112

Adjacent sequences:  A188673 A188674 A188675 * A188677 A188678 A188679

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Apr 08 2011

STATUS

approved

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Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)