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Search: id:A065980
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| A065980 |
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Inverse binomial transform of [1^1,2^2,3^3,...]. |
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+0
1
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| 1, 3, 20, 186, 2248, 33340, 585744, 11891236, 273854368, 7053523236, 200894140120, 6268924259884, 212691682554960, 7795165961244532, 306908654169113416, 12918649608270463740, 578931362074039774144
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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(0, {a(n),n=1,...}) = inverse binomial transform of {A001923(m), m=0,...} [From Tilman Neumann (Tilman.Neumann(AT)web.de), Dec 17 2008]
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LINKS
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F. Ellermann, Illustration of binomial transforms
N. J. A. Sloane, Transforms
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FORMULA
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O.g.f.: Sum_{n>0} (n*x/(1+x))^n. E.g.f.: int(-exp(-x)*LambertW(-x)/(1+LambertW(-x))^3/x, x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 12 2003
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PROGRAM
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(PARI) a(n)=if(n<1, 0, (n-1)!*polcoeff(exp(-x+O(x^n))*sum(k=0, n-1, (k+1)^(k+1)*x^k/k!), n-1))
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CROSSREFS
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Cf. A001923 [From Tilman Neumann (Tilman.Neumann(AT)web.de), Dec 17 2008]
Sequence in context: A000891 A129840 A085390 this_sequence A073767 A108206 A120485
Adjacent sequences: A065977 A065978 A065979 this_sequence A065981 A065982 A065983
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KEYWORD
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easy,nonn
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AUTHOR
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Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 09 2001
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