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A193932
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E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6).
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2
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1, 1, 3, 13, 73, 501, 4051, 32593, 313713, 3326473, 38377891, 476464341, 6299024953, 87715975933, 1314012177843, 20776583119321, 345267365639521, 6009277853650833, 109262845394221123, 2073062512187103133, 41084832105634595241, 845645768972241105541
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/6, (-1)^i*binomial(k,k-i)*binomial(n-6*i-1,k-1))/k!), n>0, a(0)=1.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 6)))
end:
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Exp[Total[x^Range[6]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 12 2015 *)
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PROG
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(Maxima)
a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-6*i-1, k-1), i, 0, (n-k)/6)/k!, k, 1, 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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