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A131127
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Table read by rows: 2*A007318(n,m) - (-1)^(n+m)*A097806(n,m).
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2
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1, 3, 1, 2, 5, 1, 2, 6, 7, 1, 2, 8, 12, 9, 1, 2, 10, 20, 20, 11, 1, 2, 12, 30, 40, 30, 13, 1, 2, 14, 42, 70, 70, 42, 15, 1, 2, 16, 56, 112, 140, 112, 56, 17, 1, 2, 18, 72, 168, 252, 252, 168, 72, 19, 1, 2, 20, 90, 240, 420, 504, 420, 240, 90, 21, 1, 2, 22, 110, 330, 660, 924, 924
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums = A000079(n+1), n>0.
Warning: row sums are not A046055! - N. J. A. Sloane, Jul 08 2009
Row sums = A151821(n+1), n>=0. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 13 2009]
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FORMULA
| 2*A007318 - A097806 (signed), A007318 = Pascal's triangle and using the signed version of the pair operator A097806 with (1,1,1,...) in the main diagonal and (-1,-1,-1,...) in the subdiagonal.
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EXAMPLE
| First few rows of the triangle are:
1;
3, 1;
2, 5, 1;
2, 6, 7, 1;
2, 8, 12, 9, 1;
2, 10, 20, 20, 11, 1;
...
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MAPLE
| T:= (n, m)-> 2 *binomial (n, m) -(-1)^(n+m) * `if`(n=m or n=m+1, 1, 0): seq (seq (T(n, m), m=0..n), n=0..12); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 13 2009]
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CROSSREFS
| Cf. A097806, A007318.
Sequence in context: A021036 A080521 A125704 * A113141 A134225 A136081
Adjacent sequences: A131124 A131125 A131126 * A131128 A131129 A131130
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 16 2007
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EXTENSIONS
| Edited by N. J. A. Sloane and R. J. Mathar, Jul 09 2009
Corrected and extended by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 13 2009
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