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A207648
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Expansion of e.g.f. Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} ((1+x)^(n+k) - 1).
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1
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1, 1, 5, 60, 1192, 34790, 1378380, 70445130, 4478636736, 344722776048, 31454679473280, 3345722335272240, 409180573835161920, 56883771843543627840, 8902319140111902785280, 1555438839901675382253600, 301239031844599064651635200, 64260075520580099615272097280
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OFFSET
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0,3
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COMMENTS
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Compare e.g.f. to: Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} (n+k)*x, which is a g.f. of Catalan numbers (A000108).
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LINKS
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FORMULA
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E.g.f.: Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} ((1+x)^(n+k) - 1).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 5*x^2/2! + 60*x^3/3! + 1192*x^4/4! + 34790*x^5/5! +...
such that, by definition,
A(x) = 1 + ((1+x)^2-1)/2! + ((1+x)^3-1)*((1+x)^4-1)/3! + ((1+x)^4-1)*((1+x)^5-1)*((1+x)^6-1)/4! + ((1+x)^5-1)*((1+x)^6-1)*((1+x)^7-1)*((1+x)^8-1)/5! +...
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PROG
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(PARI) {a(n)=n!*polcoeff(sum(m=0, n, 1/(m+1)!*prod(k=1, m, (1+x)^(m+k)-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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