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A141690
Triangle t(n,m) = 2*A008292(n+1,m+1) - A007318(n,m), a linear combination of Eulerian numbers and Pascal's triangle, 0 <= m <= n.
2
1, 1, 1, 1, 6, 1, 1, 19, 19, 1, 1, 48, 126, 48, 1, 1, 109, 594, 594, 109, 1, 1, 234, 2367, 4812, 2367, 234, 1, 1, 487, 8565, 31203, 31203, 8565, 487, 1, 1, 996, 29188, 176412, 312310, 176412, 29188, 996, 1, 1, 2017, 95644, 910300, 2620582, 2620582, 910300
OFFSET
0,5
COMMENTS
Row sums are 1, 2, 8, 40, 224, 1408, 10016, 80512, 725504, 7257088, ... = 2*(n+1)! - 2^n.
EXAMPLE
Triangle begins
1;
1, 1;
1, 6, 1;
1, 19, 19, 1;
1, 48, 126, 48, 1;
1, 109, 594, 594, 109, 1;
1, 234, 2367, 4812, 2367, 234, 1;
1, 487, 8565, 31203, 31203, 8565, 487, 1;
1, 996, 29188, 176412, 312310, 176412, 29188, 996, 1;
1, 2017, 95644, 910300, 2620582, 2620582, 910300, 95644, 2017, 1;
MAPLE
A141690 := proc(n, m)
2*A008292(n+1, m+1)-binomial(n, m) ;
end proc: # R. J. Mathar, Jul 12 2012
MATHEMATICA
Table[Table[(2*Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] - Binomial[n - 1, k]), {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]
CROSSREFS
Sequence in context: A328888 A176125 A168289 * A318408 A146957 A146988
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Sep 09 2008
STATUS
approved