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A010845
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a(n) = 3n*a(n-1) + 1, a(0) = 1.
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6
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1, 4, 25, 226, 2713, 40696, 732529, 15383110, 369194641, 9968255308, 299047659241, 9868572754954, 355268619178345, 13855476147955456, 581929998214129153, 26186849919635811886, 1256968796142518970529
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Related to Incomplete Gamma Function at 1/3.
For positive n, a(n) equals 3^n times the permanent of the nXn matrix with (4/3)'s along the main diagonal, and 1's everywhere else. [From John M. Campbell, Jul 10 2011]
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 262.
Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 262.
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FORMULA
| E.g.f.: exp(x)/(1-3*x).
a(n) = floor( e^(1/3)*n!*3^n ).
a(n) = n!*Sum(3^(n-k)/k!, k=0..n).
a(n) = n!*(e^(1/3)-Sum(3^(n-k)/k!, k=n+1...)).
a(n) = Sum[P(n, k)*3^k, {k, 0, n}]. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 29 2005
Binomial transform of A032031. - Carl Najafi, Sep 11 2011
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MATHEMATICA
| Table[ Gamma[ n, 1/3 ]*Exp[ 1/3 ]*3^(n-1), {n, 1, 24} ]
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CROSSREFS
| Cf. A000522, A010844, A056545, A056546, A056547 for analogues. a(n)/(A000142*A000244) is an increasingly good approximation to cube root of e.
Cf. A010844.
Sequence in context: A050386 A001247 A031152 * A087660 A121660 A118835
Adjacent sequences: A010842 A010843 A010844 * A010846 A010847 A010848
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KEYWORD
| easy,nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Better description and formulae from Michael Somos
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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