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A135749
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a(n) = Sum_{k=0..n} binomial(n,k)*(n-k)^k*k^k.
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1
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1, 1, 3, 19, 217, 3821, 95761, 3214975, 137501505, 7226764921, 455941716481, 33983083953611, 2954163633223969, 296027886705639973, 33823026186790043841, 4363561123325076879991, 630392564294402819207041
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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!*[x^n] Sum_{k=0..n} exp((n-k)*x)^k * x^k/k!.
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MATHEMATICA
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Table[Sum[Binomial[n, k](n-k)^k k^k, {k, n}], {n, 0, 20}]+1 (* Harvey P. Dale, Oct 08 2012 *)
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PROG
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(PARI) a(n)=sum(k=0, n, binomial(n, k)*(n-k)^k*k^k)
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp((n-k)*k*x +x*O(x^n))*x^k/k!), 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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