Search: id:A001120
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%I A001120 M2760 N1110
%S A001120 1,3,8,33,164,985,6894,55153,496376,4963761,54601370,655216441,
%T A001120 8517813732,119249392249,1788740883734,28619854139745,486537520375664,
%U A001120 8757675366761953,166395831968477106,3327916639369542121
%N A001120 a(1) = 1; for n > 1, a(n) = n*a(n-1) + (-1)^n.
%D A001120 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001120 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%F A001120 Nearest integer to n!(1+1/e).
%F A001120 a(n) = A000166(n) + n! . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Sep 04 2005
%F A001120 a(n)=n!*(1+Sum{k=0..n}{(-1)^k/k!}, with n>=1 [From Paolo P. Lava (ppl(AT)spl.at), 
               Nov 21 2008]
%o A001120 (PARI) a(n)=if(n<2,n>0,n*a(n-1)+(-1)^n)
%o A001120 (PARI) a(n)=if(n<1,0,n!*polcoeff((1+exp(-x+x*O(x^n)))/(1-x),n))
%Y A001120 A000166 has a similar recurrence.
%Y A001120 Sequence in context: A148917 A120892 A109655 this_sequence A117722 A024419 
               A094448
%Y A001120 Adjacent sequences: A001117 A001118 A001119 this_sequence A001121 A001122 
               A001123
%K A001120 nonn,easy
%O A001120 1,2
%A A001120 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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