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A277637 Partial sums of A007004. 0
1, 4, 34, 454, 7384, 133510, 2583958, 52468078, 1104191608, 23891534758, 528527606698, 11905777228618, 272269758961018, 6306419621308618, 147677930682023818, 3491114167267938298, 83217317955857060788, 1998209467779811473538, 48293984598611551487038, 1174012306200941229710038, 28689784424223599507417938 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)