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A261668
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Number of admissible words of Type G arising in study of q-analogs of multiple zeta values.
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2
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1, 8, 49, 294, 1791, 11087, 69497, 439790, 2803657, 17978388, 115837591, 749321715, 4863369655, 31655226107, 206549749929, 1350638103790, 8848643946549, 58069093513634, 381650672631329, 2511733593767294, 16550500379912639, 109176697072162079, 720921085149563159
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{1<=d,k<=n} Sum_{x1+···+xd=d+k-1 and x1,...,xd>=1} x1*x2*...*xd. See Proposition 10.8 p. 28 of Zhao link. - Michel Marcus, Sep 06 2015
a(n) = Sum_{d=1..n} binomial(2d+n-1,n-1). Also, a(n) is the coefficient of x^(2n) in ((1+x)^(-n-1)-1)/(1-x), or the coefficient of x^n in ((1+x)^(3n+1)-(1+x)^(n+1))/(2+x). - Max Alekseyev, Sep 14 2015
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MAPLE
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b:= proc(n, t) option remember; `if`(t>n or t<0, 0,
`if`(n=0, 1, add(j*b(n-j, t-1), j=1..n)))
end:
a:= n-> add(add(b(d+k-1, d), d=1..n), k=1..n):
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MATHEMATICA
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PROG
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(PARI) a(n) = polcoeff(( (1+x+O(x^(2*n+1)))^(-n-1)-1)/(1-x), 2*n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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