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Search: id:A104150
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| A104150 |
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Shifted factorial numbers: a(0)=0, a(n)=(n-1)!. |
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+0
1
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| 0, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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).
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FORMULA
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E.g.f. = -ln(1-x) = x + x^2/2 + x^3/3 + ...+ x^n/n + ...
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PROGRAM
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(Other) sage: [stirling_number1(n, 1) for n in xrange(0, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
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CROSSREFS
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Cf. A000142.
Sequence in context: A154659 A155456 A000142 this_sequence A124355 A133942 A159333
Adjacent sequences: A104147 A104148 A104149 this_sequence A104151 A104152 A104153
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Mar 08 2005
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