A188683 Alternate partial sums of binomial(3n,n)^2/(2n+1).

1, 2, 43, 965, 26260, 793559, 25715833, 875686727, 30942995146, 1125179561729, 41860674073996, 1586681151506804, 61081201435584796, 2382392690910289172, 93969463115644112428, 3742596382979058395348

Offset: 0

Author

Emanuele Munarini, Apr 08 2011

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..606

Crossrefs

Cf. A005809, A001764, A188676, A104859, A188678, A188681, A188686, A188687.

Cf. Alternate partial sums of binomial(3n,n)^2/(2n+1)^k: A188680 (k=0), this sequence (k=1), A188685 (k=2).

Cf. Partial sums of binomial(3n,n)^2/(2n+1)^k: A188679 (k=0), A188682 (k=1), A188684 (k=2).

Programs

Mathematica

Table[Sum[Binomial[3k,k]^2(-1)^(n-k)/(2k+1),{k,0,n}],{n,0,20}]

Maxima

makelist(sum(binomial(3*k,k)^2*(-1)^(n-k)/(2*k+1),k,0,n),n,0,20);

Formula

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

Recurrence: 4*(n+2)^2*(4*n^2+16*n+15) * a(n+2) -(713*n^4+4246*n^3 +9421*n^2 +9224*n+3360) * a(n+1) -9*(9*n^2+27*n+20)^2 * a(n) = 0.

a(n) ~ 3^(6*n+7)/(745*Pi*n^2*2^(4*n+3)). - Vaclav Kotesovec, Aug 06 2013