A174966 A symmetrical triangle sequence: q=1;t(n,m,q)=If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]]

1, 1, 1, 1, -2, 1, 1, -19, -19, 1, 1, -74, -324, -74, 1, 1, -223, -2708, -2708, -223, 1, 1, -594, -16659, -45884, -16659, -594, 1, 1, -1475, -85839, -531011, -531011, -85839, -1475, 1, 1, -3506, -394388, -4852814, -10777040, -4852814, -394388, -3506, 1, 1

Offset

0,5

Comments

Row sums are:

{1, 2, 0, -36, -470, -5860, -80388, -1236648, -21278454, -406514868,

-8555215724,...}.

Links

Table of n, a(n) for n=0..45.

Formula

q=1;

t(n,m,q)=If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]]

Example

{1},
{1, 1},
{1, -2, 1},
{1, -19, -19, 1},
{1, -74, -324, -74, 1},
{1, -223, -2708, -2708, -223, 1},
{1, -594, -16659, -45884, -16659, -594, 1},
{1, -1475, -85839, -531011, -531011, -85839, -1475, 1},
{1, -3506, -394388, -4852814, -10777040, -4852814, -394388, -3506, 1},
{1, -8095, -1674364, -37780852, -163794124, -163794124, -37780852, -1674364, -8095, 1},
{1, -18314, -6715983, -262214952, -2035265616, -3946785996, -2035265616, -262214952, -6715983, -18314, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_, q_] = If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[ n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]];
Table[Table[Sum[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 10}]

Crossrefs

Cf. A174912, A174914

Sequence in context: A090163 A179071 A124001 * A157453 A174174 A156889

Adjacent sequences: A174963 A174964 A174965 * A174967 A174968 A174969

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 02 2010

Status

approved