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 A007116 Expansion of e.g.f. (1+x)^(exp(x)). (Formerly M1634) 3
 1, 1, 2, 6, 18, 75, 295, 1575, 7196, 48993, 230413, 2164767, 8055938, 139431149, 70125991, 14201296057, -77573062280, 2389977322593, -28817693086263, 615493949444827, -10403976760589602, 215611836994976237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..451 FORMULA a(n) = sum(k=1..n, sum(i=0..n-k, binomial(n,i)*k^i*Stirling1(n-i,k))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011 |a(n)| ~ n!/(Gamma(-exp(-1))*n^(1+exp(-1))). - Vaclav Kotesovec, Jun 27 2013 MATHEMATICA With[{nn=25}, CoefficientList[Series[(1+x)^Exp[x], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Sep 21 2011 *) PROG (Maxima) a(n):=sum(sum(binomial(n, i)*k^i*stirling1(n-i, k), i, 0, n-k), k, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */ CROSSREFS Cf. A002741, A009198, A191365. Sequence in context: A277862 A213427 A006388 * A280763 A079391 A162058 Adjacent sequences: A007113 A007114 A007115 * A007117 A007118 A007119 KEYWORD sign,easy AUTHOR EXTENSIONS Definition and terms corrected, and more terms added by Joerg Arndt, Jun 01 2011 STATUS approved

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Last modified December 6 15:48 EST 2022. Contains 358644 sequences. (Running on oeis4.)