A178347 Triangle t(n,m,k) = binomial(n, m) - k*(binomial(n, m)*binomial(n+1, m)/(m+1)) + k*Eulerian(n+1, m) with k = 6.

1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 100, 282, 100, 1, 1, 257, 1522, 1522, 257, 1, 1, 600, 6531, 13466, 6531, 600, 1, 1, 1321, 24603, 90809, 90809, 24603, 1321, 1, 1, 2804, 85660, 522404, 926626, 522404, 85660, 2804, 1, 1, 5817, 283836, 2716116, 7830498

Offset

0,5

Links

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

Example

{1},
{1, 1},
{1, 8, 1},
{1, 33, 33, 1},
{1, 100, 282, 100, 1},
{1, 257, 1522, 1522, 257, 1},
{1, 600, 6531, 13466, 6531, 600, 1},
{1, 1321, 24603, 90809, 90809, 24603, 1321, 1},
{1, 2804, 85660, 522404, 926626, 522404, 85660, 2804, 1},
{1, 5817, 283836, 2716116, 7830498, 7830498, 2716116, 283836, 5817, 1},
{1, 11896, 910917, 13191348, 58345734, 94229316, 58345734, 13191348, 910917, 11896, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_, k_] = Binomial[n, m] - k*(Binomial[n, m]* Binomial[n + 1, m]/(m + 1)) + k*Eulerian[n + 1, m];
Table[Flatten[Table[Table[t[n, m, k], {m, 0, n}], {n, 0, 10}]], {k, 0, 10}]

Crossrefs

Sequence in context: A168523 A144439 A157208 * A141686 A185412 A157148

Adjacent sequences: A178344 A178345 A178346 * A178348 A178349 A178350

Keyword

nonn,tabl,less

Author

Roger L. Bagula, May 25 2010

Status

approved