A141691 A linear combination of Eulerian numbers (A008292) and Pascal's triangle (A007318); t(n,m)=(3*A008292(n,m)-A007318(n,m))/2.

1, 1, 1, 1, 5, 1, 1, 15, 15, 1, 1, 37, 96, 37, 1, 1, 83, 448, 448, 83, 1, 1, 177, 1779, 3614, 1779, 177, 1, 1, 367, 6429, 23411, 23411, 6429, 367, 1, 1, 749, 21898, 132323, 234250, 132323, 21898, 749, 1, 1, 1515, 71742, 682746, 1965468, 1965468, 682746, 71742

Offset

1,5

Comments

Row sums are:

{1, 2, 7, 32, 172, 1064, 7528, 60416, 544192, 5442944}.

Links

Table of n, a(n) for n=1..53.

Formula

t(n,m)=(3*A008292(n,m)-A007318(n,m))/2.

Example

{1},
{1, 1},
{1, 5, 1},
{1, 15, 15, 1},
{1, 37, 96, 37, 1},
{1, 83, 448, 448, 83, 1},
{1, 177, 1779, 3614, 1779, 177, 1},
{1, 367, 6429, 23411, 23411, 6429, 367, 1},
{1, 749, 21898, 132323, 234250, 132323, 21898, 749, 1},
{1, 1515, 71742, 682746, 1965468, 1965468, 682746, 71742, 1515, 1}

Mathematica

Table[Table[((2*Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] - Binomial[n - 1, k]) + Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}])/2, {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]

Crossrefs

Cf. A008292, A007318.

Sequence in context: A056940 A168288 A157523 * A157147 A347973 A232103

Adjacent sequences: A141688 A141689 A141690 * A141692 A141693 A141694

Keyword

nonn,uned

Author

Roger L. Bagula, Sep 09 2008

Status

approved