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Search: id:A032443
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| A032443 |
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Sum(binomial(2*n,i),i=0..n). |
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+0
15
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| 1, 3, 11, 42, 163, 638, 2510, 9908, 39203, 155382, 616666, 2449868, 9740686, 38754732, 154276028, 614429672, 2448023843, 9756737702, 38897306018, 155111585372, 618679078298, 2468152192772
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Array interpretation : first row is filled with 1's, first column with powers of 2, b(i,j)=b(i-1,j)+b(i,j-1); then a(n)=b(n,n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 01 2002
1 1 1 1 1 1 1 ...
2 3 4 5 6 7 8 ...
4 7 11 16 22 ....
8 15 26 42 64....
16 31 ..99 163...
Hankel transform is n+1. - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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REFERENCES
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A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, preprint, 2007.
M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.
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FORMULA
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(4^n+binomial(2*n, n))/2 (David W. Wilson)
a(n)=sum_{0<=i_1<=i_2<=n}binomial(n, i_2)*binomial(n, i_1+i_2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 14 2004
Sequence with interpolated zeros has a(n)=sum{k=0..floor(n/2), if(mod(n-2k, 2)=0, C(n, k), 0)}. - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005
a(n)=sum{k=0..n, C(n+k-1,k)2^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Sep 28 2007
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CROSSREFS
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Binomial transform of A027914. Hankel transform is {1, 2, 3, 4, ..., n, ...} - John W. Layman (layman(AT)math.vt.edu), Aug 04 2000
Sequence in context: A106460 A059716 A122368 this_sequence A117641 A084782 A066655
Adjacent sequences: A032440 A032441 A032442 this_sequence A032444 A032445 A032446
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KEYWORD
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nonn
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AUTHOR
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J. H. Conway (conway(AT)math.princeton.edu)
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