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Search: id:A111961
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| A111961 |
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Expansion of 1/(sqrt(1-2x-3x^2)-x). |
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+0
3
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| 1, 2, 6, 18, 56, 176, 558, 1778, 5686, 18230, 58558, 188366, 606588, 1955044, 6305418, 20347342, 65689088, 212146400, 685342218, 2214556478, 7157409064, 23136645472, 74801223162, 241863933094, 782131232390, 2529458676326
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums of A111960.
A transform of the Fibonacci numbers. - Paul Barry (pbarry(AT)wit.ie), Sep 23 2005
Apparently the Motzkin transform of (0 followed by A128588). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 11 2008]
Inverse binomial transform of A026671. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 11 2009]
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FORMULA
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a(n)=sum{k=0..n, sum{j=0..n, C(n, j)*C((j-1)/2, (j-k)/2)*2^(j-k)*(1+(-1)^(j-k))/2}}
a(n)=sum{k=0..n, F(k+1)*sum{i=0..floor((n-k)/2), C(n, i)C(n-i, i+k)/(i+k+1)}}. - Paul Barry (pbarry(AT)wit.ie), Sep 23 2005
G.f.: M(x)^2/(2*M(x)-M(x)^2), where M(x) is the g.f. of the Motzkin numbers A001006; - Paul Barry (pbarry(AT)wit.ie), Feb 03 2006
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CROSSREFS
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Sequence in context: A148457 A002999 A091142 this_sequence A071721 A125306 A064310
Adjacent sequences: A111958 A111959 A111960 this_sequence A111962 A111963 A111964
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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), Aug 23 2005
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