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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are 1, 2, 8, 40, 224, 1408, 10016, 80512, 725504, 7257088, ... = 2*(n+1)! - 2^n.

LINKS

G. C. Greubel, Rows n=0..100 of triangle, flattend

EXAMPLE

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

Cf. A008292, A007318.

Sequence in context: A328888 A176125 A168289 * A318408 A146957 A146988

Adjacent sequences:  A141687 A141688 A141689 * A141691 A141692 A141693

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Sep 09 2008

STATUS

approved

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)