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Search: id:A056546
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| A056546 |
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a(n) = 5n * a(n-1) +1 with a(0)=1. |
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+0
4
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| 1, 6, 61, 916, 18321, 458026, 13740781, 480927336, 19237093441, 865669204846, 43283460242301, 2380590313326556, 142835418799593361, 9284302221973568466, 649901155538149792621, 48742586665361234446576
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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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FORMULA
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a(n) = floor[ e^(1/5)*5^n*n! ]
a(n) = n!*sum(5^(n-k)/k!, k=0..n) . E.g.f. : exp(x) / (1-5x) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 14 2004
a(n) = Sum[P(n, k)5^k, {k, 0, n}]. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 29 2005
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EXAMPLE
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a(2)=5*2*a(1)+1=10*6+1=61
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CROSSREFS
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Cf. A000522, A010844, A010845, A056545, A056547 for analogues. A056546/(A000142*A000351) is an increasingly good approximation to 5th root of e.
Sequence in context: A047737 A086403 A049120 this_sequence A127695 A144343 A022517
Adjacent sequences: A056543 A056544 A056545 this_sequence A056547 A056548 A056549
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottonley (se16(AT)btinternet.com), Jun 20 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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