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 A067078 a(1) = 1, a(2) = 2, a(n) = (n-1)*a(n-1) - (n-2)*a(n-2). 4
 1, 2, 3, 5, 11, 35, 155, 875, 5915, 46235, 409115, 4037915, 43954715, 522956315, 6749977115, 93928268315, 1401602636315, 22324392524315, 378011820620315, 6780385526348315, 128425485935180315, 2561327494111820315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Successive differences are factorials, or (n+1)st successive difference divided by n-th successive difference = n. I.e., {a(n+2)-a(n+1)}/{a(n+1)-a(n)} = n. - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 14 2003 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..100 FORMULA a(n) =1+sum_{0<=i<=n-2} i! =2*A014288(n-1)+1 =A007489(n-2)+2 (n>1). - Henry Bottomley, Oct 23 2002; corrected by M. F. Hasler, Dec 16 2007 a(n) = 1+!(n-1) = 1+A003422(n-1); a(n+1)=a(n)+(n-1)!. - M. F. Hasler, Dec 16 2007 E.g.f. A(x)=x*B(x) satisfies the differential equation B'(x)=B(x)+log(1/(1-x))+1. - Vladimir Kruchinin, Jan 19 2011 EXAMPLE a(6) = 35, a(5)= 11 hence a(7) = 6*35 - 5*11 = 155. MATHEMATICA a[1] = 1; a[2] = 2; a[n_] := a[n] = (n - 1)*a[n - 1] - (n - 2)*a[n - 2]; Table[ a[n], {n, 1, 25} ] a=FoldList[Plus, 2, (Range@40)! ]; PrependTo[a, 1] (* Vladimir Joseph Stephan Orlovsky, May 21 2010 *) PROG (PARI) A067078(n)=sum(k=0, n-2, k!, 1) \\ M. F. Hasler, Dec 16 2007 (Haskell) a067078 n = a067078_list !! (n-1) a067078_list = scanl (+) 1 a000142_list -- Reinhard Zumkeller, Dec 27 2011 CROSSREFS Cf. A003422, A014288, A007489. From Johannes W. Meijer, Oct 16 2009: (Start) Equals the row sums of A165680. (End) Sequence in context: A305971 A064095 A061935 * A124561 A167604 A065510 Adjacent sequences:  A067075 A067076 A067077 * A067079 A067080 A067081 KEYWORD nonn AUTHOR Amarnath Murthy, Jan 05 2002 EXTENSIONS More terms from Robert G. Wilson v, Jan 07 2002 Edited by M. F. Hasler, Dec 16 2007 STATUS approved

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Last modified July 22 14:31 EDT 2019. Contains 325222 sequences. (Running on oeis4.)