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Search: id:A084152
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| A084152 |
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Exponential self-convolution of Jacobsthal numbers (divided by 2). |
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+0
4
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| 0, 0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575, 244335800775, 977343902151, 3909374210503, 15637499638215, 62549992960455
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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a(n)=(4^n-2+(-2)^n)/18; G.f.: x^2/((1-x)(1+2x)(1-4x)); E.g.f. : (exp(2x)-exp(-x))^2/18=(exp(4x)-2exp(x)+exp(-x))/18.
Binomial transform of 0, 0, 1, 0, 9, 0, 81, ... a(n)=A001045(n)*A078008(n)/2.
a(n)=floor(2^n/3)ceiling(2^n/3)/2 - Paul Barry (pbarry(AT)wit.ie), Apr 28 2004
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 2, -2) for n in xrange(0, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
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Cf. A001045, A084153.
Except for initial terms, same as A015249 and A084175.
Sequence in context: A152896 A007973 A015249 this_sequence A084175 A081951 A033853
Adjacent sequences: A084149 A084150 A084151 this_sequence A084153 A084154 A084155
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 16 2003
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