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A207570
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G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^(3*k-2) - 1).
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3
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1, 1, 4, 34, 410, 6455, 125251, 2888305, 77157780, 2342972405, 79701049425, 3002132647515, 124039845584382, 5577660227565634, 271162541308698623, 14172237715785139175, 792418822364402364530, 47198077739119663907870, 2983413619934353599892285
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OFFSET
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0,3
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COMMENTS
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Compare g.f. to: Sum_{n>=0} Product_{k=1..n} ((1+x)^k - 1), which is the g.f. of A179525.
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LINKS
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FORMULA
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a(n) ~ GAMMA(2/3) * 2^(2*n-1/3) * 3^(2*n+5/6) * n^(n-1/6) / (exp(n+Pi^2/72) * Pi^(2*n+7/6)). - Vaclav Kotesovec, May 06 2014
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 34*x^3 + 410*x^4 + 6455*x^5 + 125251*x^6 +...
such that, by definition,
A(x) = 1 + ((1+x)-1) + ((1+x)-1)*((1+x)^4-1) + ((1+x)-1)*((1+x)^4-1)*((1+x)^7-1) + ((1+x)-1)*((1+x)^4-1)*((1+x)^7-1)*((1+x)^10-1) +...
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MATHEMATICA
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Join[{1}, Rest[With[{nn=20}, CoefficientList[Series[Sum[Product[ (1+x)^(3k-2)-1, {k, n}], {n, nn}], {x, 0, nn}], x]]]] (* Harvey P. Dale, Aug 20 2012 *)
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PROG
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(PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, (1+x)^(3*k-2)-1) +x*O(x^n)), n)}
for(n=0, 25, print1(a(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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STATUS
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approved
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