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Search: id:A115205
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| A115205 |
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Toral inverse of multiplicative persistence based on A035927. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 56, 221, 716, 2003, 5006, 11441, 24311, 48621, 92379, 167961, 293931, 497421, 817191, 1307505
(list; graph; listen)
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OFFSET
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0,10
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COMMENT
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A method I came up with of generating new sequences from old using the z transform and its inverse using the f[x]->f[1/x] transform ( toral inverse).
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REFERENCES
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http://mathworld.wolfram.com/MultiplicativePersistence.html
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FORMULA
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f[x_] = ZTransform[binomial[10 + n - 1, n] - 1, n, x] a(n) = InverseZTransform[f[1/x], x, n]
Conjecture: G.f.:((3*x^2-3*x+1)*(3*x^6-9*x^5+18*x^4-21*x^3+15*x^2-6*x+1))/(x-1)^10 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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MAPLE
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seq(binomial(n, 9)+1, n=0..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 13 2007
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MATHEMATICA
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f[x_] = ZTransform[Binomial[10 + n - 1, n] - 1, n, x] g[n_] = InverseZTransform[f[1/x], x, n] a = Table[g[n], {n, 1, 25}]
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CROSSREFS
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Cf. A035927.
Sequence in context: A128748 A037522 A037731 this_sequence A037554 A106804 A041129
Adjacent sequences: A115202 A115203 A115204 this_sequence A115206 A115207 A115208
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 03 2006
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