A155452 Triangle read by rows: let t1(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]; then T(n,m)=2*t1(n + 1, k) - (m! - n! + (-m + n)!).

1, 1, 1, 1, 8, 1, 1, 25, 25, 1, 1, 69, 152, 69, 1, 1, 209, 716, 716, 209, 1, 1, 839, 3076, 5540, 3076, 839, 1, 1, 4813, 13504, 36248, 36248, 13504, 4813, 1, 1, 36283, 68814, 216662, 352652, 216662, 68814, 36283, 1, 1, 324585, 453518, 1272538, 2983444

Offset

0,5

Comments

Row sums are {1, 2, 10, 52, 292, 1852, 13372, 109132, 996172, 10068172, 111674572,...}.

Links

Table of n, a(n) for n=0..49.

Example

{1},
{1, 1},
{1, 8, 1},
{1, 25, 25, 1},
{1, 69, 152, 69, 1},
{1, 209, 716, 716, 209, 1},
{1, 839, 3076, 5540, 3076, 839, 1},
{1, 4813, 13504, 36248, 36248, 13504, 4813, 1},
{1, 36283, 68814, 216662, 352652, 216662, 68814, 36283, 1},
{1, 324585, 453518, 1272538, 2983444, 2983444, 1272538, 453518, 324585, 1},
{1, 3269991, 3893752, 8030730, 23104284, 35077056, 23104284, 8030730, 3893752, 3269991, 1}

Mathematica

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

Crossrefs

Sequence in context: A144436 A358628 A167034 * A147295 A174388 A220718

Adjacent sequences: A155449 A155450 A155451 * A155453 A155454 A155455

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 22 2009

Extensions

Edited by N. J. A. Sloane, Jan 25 2009

Status

approved