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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, rowsum 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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