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Search: id:A127905
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| A127905 |
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Construct triangle in which n-th row is obtained by expanding (1+x+x^3)^n and take the next-to-central column. |
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+0
1
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| 0, 1, 2, 3, 8, 25, 66, 168, 456, 1269, 3490, 9581, 26544, 73944, 206220, 576045, 1613264, 4527661, 12725946, 35818135, 100950440, 284869263, 804726934, 2275500998, 6440230392, 18242735800, 51714552656
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=n*A071879(n-1).
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FORMULA
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a(n)=n*sum{k=0..floor((n-1)/3), C(n-1,3k)*C(3k,k)/(2k+1)}; a(n)=sum{k=0..floor((n-1)/3), (3k+1)*C(n,3k+1)*C(3k,k)/(2k+1)}; a(n)=sum{k=0..n-1, sum{j=0..floor(k/3), C(k,3j)*C(3j+1,j)}};
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff((1+x+x^3)^n, n-1)); (PARI) a(n)=if(n<0, 0, n++; n*polcoeff(serreverse(x/(1+x+x^3)+x*O(x^n)), n)).
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CROSSREFS
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Cf. A005717.
Sequence in context: A120260 A002619 A129202 this_sequence A009224 A065619 A111121
Adjacent sequences: A127902 A127903 A127904 this_sequence A127906 A127907 A127908
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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), Feb 05 2007
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EXTENSIONS
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Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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