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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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OFFSET
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0,2
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LINKS
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FORMULA
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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).
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MATHEMATICA
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Table[Sum[Multinomial[k, k, k]/(k + 1), {k, 0, n}], {n, 0, 100}]
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PROG
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(Maxima) makelist(sum(multinomial_coeff(k, k, k)/(k+1), k, 0, n), n, 0, 12);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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