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Search: id:A110441
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| A110441 |
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Triangular array formed by the Mersenne numbers. |
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+0
2
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| 1, 3, 1, 7, 6, 1, 15, 23, 9, 1, 31, 72, 48, 12, 1, 63, 201, 198, 82, 15, 1, 127, 522, 699, 420, 125, 18, 1, 255, 1291, 2223, 1795, 765, 177, 21, 1, 511, 3084, 6562, 6768, 3840, 1260, 238, 24, 1, 1023, 7181, 18324, 23276, 16758, 7266, 1932, 308, 27, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence factors A038255 into a product of Riordan arrays.
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REFERENCES
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Naiomi T. Cameron and Asamoah Nkwanta, On Some (Pseudo) Involutions in the Riordan Group, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.7.
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FORMULA
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Riordan array M(n, k): (1/(1-3z+2z^2), z/(1-3z+2z^2)). Leftmost column M(n, 0) is the Mersenne numbers A000225, first column is A045618, second column is A055582, row sum is A007070 and diagonal sum is even indexed Fibonacci numbers A001906.
T(n,k)=sum{j=0..n, C(j+k,k)C(n-j,k)2^(n-j-k)} - Paul Barry (pbarry(AT)wit.ie), Feb 13 2006
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EXAMPLE
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Triangle starts:
1;
3,1;
7,6,1;
15,23,9,1;
31,72,48,12,1;
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CROSSREFS
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Sequence in context: A138257 A071043 A101624 this_sequence A111806 A054458 A110168
Adjacent sequences: A110438 A110439 A110440 this_sequence A110442 A110443 A110444
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Asamoah Nkwanta (nkwanta(AT)jewel.morgan.edu), Aug 08 2005
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