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Search: id:A081341
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| A081341 |
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Expansion of exp(3x)cosh(3x). |
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+0
6
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| 1, 3, 18, 108, 648, 3888, 23328, 139968, 839808, 5038848, 30233088, 181398528, 1088391168, 6530347008, 39182082048, 235092492288, 1410554953728, 8463329722368, 50779978334208, 304679870005248, 1828079220031488
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A081341. 3rd binomial transform of (1,0,9,0,81,0,729,0,..).
For m>1, n>0, A166469(A002110(m)*a(n))=(n+1)*A000045(m+1). For n>0, A166469(a(n))=2n. [From Matthew Vandermast (ghodges14(AT)comcast.net), Nov 05 2009]
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FORMULA
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a(0)=1, a(n)=6^n/2, n>0 G.f.: (1-3x)/(1-6x). E.g.f. exp(3x)cosh(3x).
a(n)=A000244(n)*A011782(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]
((3+sqrt9)^n+(3-sqrt9)^n/2 in Fibonacci form [From Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008]
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MAPLE
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with(finance):seq(ceil(futurevalue(3, 5, n)), n=-1..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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PROGRAM
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(Other) SAGE:[(lucas_number2((n+1), 2, 0)*lucas_number2(n, 3, 0))/4 for n in xrange(0, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
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CROSSREFS
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Cf. A034494, A081342.
Sequence in context: A025595 A151331 A137962 this_sequence A132900 A050623 A037760
Adjacent sequences: A081338 A081339 A081340 this_sequence A081342 A081343 A081344
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 18 2003
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