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 A001120 a(0) = a(1) = 1; for n > 1, a(n) = n*a(n-1) + (-1)^n. (Formerly M2760 N1110) 6
 1, 1, 3, 8, 33, 164, 985, 6894, 55153, 496376, 4963761, 54601370, 655216441, 8517813732, 119249392249, 1788740883734, 28619854139745, 486537520375664, 8757675366761953, 166395831968477106, 3327916639369542121, 69886249426760384540, 1537497487388728459881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 (terms n = 1..100 from T. D. Noe) J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017] FORMULA Nearest integer to n!(1+1/e). a(n) = A000166(n) + [n > 0] * n!. - Philippe Deléham, Sep 04 2005 a(n) = n!*(1+Sum_{k=0..n} (-1)^k/k!, n>=1. - Paolo P. Lava, Nov 21 2008 a(n) = (n-1)*(a(n-1)+a(n-2)), n>2. - Gary Detlefs, Apr 11 2010 E.g.f.: (exp(x)*x+1)*exp(-x)/(1-x). - Alois P. Heinz, May 08 2020 MAPLE a:= proc(n) option remember;      `if`(n<2, 1, n*a(n-1)+(-1)^n)     end: seq(a(n), n=0..23);  # Alois P. Heinz, May 09 2020 MATHEMATICA t = {1}; Do[AppendTo[t, n*t[[-1]] + (-1)^n], {n, 2, 20}]; t (* T. D. Noe, Jun 26 2012 *) RecurrenceTable[{a[1]==1, a[n]==n a[n-1]+(-1)^n}, a, {n, 30}] (* Harvey P. Dale, Feb 19 2018 *) PROG (PARI) a(n)=if(n<2, n>0, n*a(n-1)+(-1)^n) (PARI) a(n)=if(n<1, 0, n!*polcoeff((1+exp(-x+x*O(x^n)))/(1-x), n)) CROSSREFS A000166 has a similar recurrence. Column k=1 of A334715. Cf. A000142. Sequence in context: A225688 A109655 A184255 * A302629 A339315 A322303 Adjacent sequences:  A001117 A001118 A001119 * A001121 A001122 A001123 KEYWORD nonn,easy AUTHOR EXTENSIONS a(0)=1 prepended by Alois P. Heinz, May 08 2020 STATUS approved

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Last modified November 26 08:23 EST 2022. Contains 358354 sequences. (Running on oeis4.)