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A261833
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a(n) = sum(stirling2(n,k)*(k+1)!*(k+3)!,k=1..n)/48.
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3
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1, 16, 406, 14866, 740026, 48026266, 3937533706, 397912444666, 48589663862026, 7053101481134266, 1200393616793282506, 236747809664852265466, 53564655768153719942026, 13780851677757681289022266, 4000515700684222714620799306, 1301419578177153109817779142266, 471541578407011294721978551670026
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OFFSET
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1,2
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COMMENTS
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It appears that for all n>1 the last digit of a(n) is 6.
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LINKS
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FORMULA
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Representation as a sum of infinite series of special values of hypergeometric functions of type 2F0, in Maple notation:
a(n) = sum(k^n*(k+1)!*(k+3)!*hypergeom([k+2,k+4],[],-1)/k!, k=1..infinity)/48, n=1,2,... .
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MAPLE
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with(combinat): a:= n-> sum(stirling2(n, k)*(k+1)!*(k+3)!, k=1..n)/48: seq(a(n), n=1..20);
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MATHEMATICA
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Table[Sum[StirlingS2[n, k]*(k+1)!*(k+3)!, {k, 1, n}]/48, {n, 1, 20}] (* Vaclav Kotesovec, Oct 05 2015 *)
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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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