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Search: id:A112657
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| A112657 |
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A Motzkin transform of Jacobsthal numbers. |
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+0
5
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| 1, 2, 7, 23, 79, 272, 943, 3278, 11419, 39830, 139057, 485795, 1697905, 5936348, 20760271, 72615143, 254028355, 888758030, 3109714117, 10881403229, 38077702909, 133251869648, 466325356273, 1631981113112, 5711490384901
(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 A100098.
Inverse binomial transform of A007854 . The Hankel transform of this sequence is 3^n (see A000244) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2007
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FORMULA
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a(n)=sum{k=0..n, A026300(n, k)(2^(k+1)+(-1)^k)/3}, where A026300 is the Motzkin triangle; a(n)=sum{k=0..n, ((k+1)/(n+1))*sum(j=0..n+1, C(n+1, j)C(j, 2j-n+k)(2^(k+1)+(-1)^k)/3}}.
a(n)=Sum_{k, 0<=k<=n}A089942(n,k)*2^k = Sum_{k, 0<=k<=n}A071947(n,k)*2^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 31 2007
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CROSSREFS
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Sequence in context: A067324 A091702 A068593 this_sequence A007717 A130567 A143629
Adjacent sequences: A112654 A112655 A112656 this_sequence A112658 A112659 A112660
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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), Jan 11 2006
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