Search: id:A104150
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%I A104150
%S A104150 0,1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,
%T A104150 6227020800,87178291200,1307674368000,20922789888000,355687428096000,
%U A104150 6402373705728000,121645100408832000,2432902008176640000
%N A104150 Shifted factorial numbers: a(0)=0, a(n)=(n-1)!.
%C A104150 E.g.f. = Sum{n=1,2..}(n-1)!*x^n/n! = Sum{n=1,2..}x^n/n The shift law 
               of the E.g.f.: if Sum{n=0,1,2..}a(n)*x^n/n! = f(x), then Sum{n=0,
               1,2..}a(n+1)*x^n/n! = d/dx f(x) and Sum{n=1,2..}a(n-1)*x^n/n! = integral 
               f(x). E.g.f. of A000142 (= n!) is 1/(1-x), so E.g.f. of a(n)=(n-1)! 
               is integral 1/(1-x) = -ln(1-x).
%F A104150 E.g.f. = -ln(1-x) = x + x^2/2 + x^3/3 + ...+ x^n/n + ...
%o A104150 (Other) sage: [stirling_number1(n,1) for n in xrange(0, 22)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
%Y A104150 Cf. A000142.
%Y A104150 Sequence in context: A154659 A155456 A000142 this_sequence A124355 A133942 
               A159333
%Y A104150 Adjacent sequences: A104147 A104148 A104149 this_sequence A104151 A104152 
               A104153
%K A104150 easy,nonn
%O A104150 0,4
%A A104150 Miklos Kristof (kristmikl(AT)freemail.hu), Mar 08 2005

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