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Search: id:A113682
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| A113682 |
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Expansion of 2/(sqrt(1-2x-3x^2)(1+x+sqrt(1-2x-3x^2))). |
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+0
4
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| 1, 1, 4, 9, 26, 70, 197, 553, 1570, 4476, 12827, 36894, 106471, 308113, 893804, 2598313, 7567466, 22076404, 64498427, 188689684, 552675365, 1620567763, 4756614062, 13974168190, 41088418151, 120906613075, 356035078102
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Convolution of A002426 and A005043. Diagonal sums of A094531.
Hankel transform is A164611. [From Paul Barry (pbarry(AT)wit.ie), Aug 17 2009]
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FORMULA
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a(n)=sum{k=0..floor(n/2), sum{i=0..n-k, C(n-2k-i, i)C(n-k, k+i)}}; a(n)=sum{k=0..n, A002426(k)A005043(n-k)}=sum{k=0..n, A005043(k)A002426(n-k)}.
a(n)=sum{k=0..n, C(n+1,k+1)C(k,n-k)} - Paul Barry (pbarry(AT)wit.ie), Aug 21 2007
a(n)=(A002426(n+1)+(-1)^n)/2. [From Paul Barry (pbarry(AT)wit.ie), Aug 17 2009]
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CROSSREFS
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Sequence in context: A087361 A090117 A020181 this_sequence A145855 A099615 A114618
Adjacent sequences: A113679 A113680 A113681 this_sequence A113683 A113684 A113685
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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), Nov 04 2005
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