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a(n) ~ 3^(3*n+7/2) / (52*Pi*n^2). - Vaclav Kotesovec, Oct 30 2016
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a(n) = sum_Sum_{k=0..n} multinomial(k,k,k)/(k+1).
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).
G.f. : hypergeometric(1/3,2/3;2;27*t)/(1-t).
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1, 4, 34, 454, 7384, 133510, 2583958, 52468078, 1104191608, 23891534758, 528527606698, 11905777228618, 272269758961018, 6306419621308618, 147677930682023818, 3491114167267938298, 83217317955857060788, 1998209467779811473538, 48293984598611551487038, 1174012306200941229710038, 28689784424223599507417938
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Cf. A007004.
Partial sums of sequence A007004.
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