A277637 Partial sums of A007004.

1, 4, 34, 454, 7384, 133510, 2583958, 52468078, 1104191608, 23891534758, 528527606698, 11905777228618, 272269758961018, 6306419621308618, 147677930682023818, 3491114167267938298, 83217317955857060788, 1998209467779811473538, 48293984598611551487038, 1174012306200941229710038, 28689784424223599507417938

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} multinomial(k,k,k)/(k+1).

Recurrence: (n+2)*(n+3)*a(n+2)-(28*n^2+86*n+66)*a(n+1)+3*(3*n+5)*(3*n+4)*a(n)=0.

a(n) = hypergeometric(1/3,2/3;2;27)-(multinomial(n+1,n+1,n+1)/(n+2)) * hypergeometric[1,n+4/3,n+5/3;n+2,n+3;27).

a(n) = 0 (mod 2) and a(n) = 1 (mod 3), for all natural n.

G.f.: hypergeometric(1/3,2/3;2;27*t)/(1-t).

a(n) ~ 3^(3*n+7/2) / (52*Pi*n^2). - Vaclav Kotesovec, Oct 30 2016

Mathematica

Table[Sum[Multinomial[k, k, k]/(k + 1), {k, 0, n}], {n, 0, 100}]

Prog

(Maxima) makelist(sum(multinomial_coeff(k, k, k)/(k+1), k, 0, n), n, 0, 12);

Crossrefs

Cf. A007004.

Sequence in context: A071213 A052629 A151919 * A218674 A321264 A234291

Adjacent sequences: A277634 A277635 A277636 * A277638 A277639 A277640

Keyword

nonn

Author

Emanuele Munarini, Oct 25 2016

Status

approved