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Search: id:A034870
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| A034870 |
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Even-numbered rows of Pascal's triangle. |
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+0
9
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| 1, 1, 2, 1, 1, 4, 6, 4, 1, 1, 6, 15, 20, 15, 6, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1, 1
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequence of row lengths of this array is [1,3,5,7,9,11,13,...]= A005408(n), n>=0.
Equals X^n * [1,0,0,0,...] where X = an infinite tridiagonal matrix with (1,1,1,...) in the main and subsubdiagonal and (2,2,2,...) in the main diagonal. X also = a triangular matrix with (1,2,1,0,0,0,...) in each column. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 26 2008
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LINKS
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W. Lang, First 9 rows.
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FORMULA
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a(n, m)=binomial(2*n, m), 0<= m <= 2*n, 0<=n, else 0.
G.f. for column m=2*k sequence: (x^k)*Pe(k, x)/(1-x)^(2*k+1), k>=0; for column m=2*k-1 sequence (x^k)*Po(k, x)/(1-x)^(2*k), k>=1, with the row polynomials Pe(k, x) := sum(A091042(k, m)*x^m, m=0..k) and Po(k, x) := 2*sum(A091044(k, m)*x^m, m=0..k-1), See also triangle A091043.
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CROSSREFS
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Cf. A007318.
Cf. A000302 (row sums, powers of 4), alternating row sums are 0, except for n=0 which gives 1.
Sequence in context: A134172 A078047 A090668 this_sequence A011016 A096540 A107386
Adjacent sequences: A034867 A034868 A034869 this_sequence A034871 A034872 A034873
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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njas
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