A174005 An antidiagonal triangle based on: t(n,q) = If[n == 0, 1, Sum[Eulerian[n, k]*q^n, {k, 1, n, 2}]].

1, 1, 1, 4, 2, 1, 12, 8, 3, 1, 52, 30, 12, 4, 1, 360, 260, 60, 16, 5, 1, 2656, 2562, 780, 108, 20, 6, 1, 20160, 23408, 8568, 1768, 180, 24, 7, 1, 177472, 262950, 94752, 20580, 3380, 282, 28, 8, 1, 1814400, 3594620, 1467840, 277984, 41160, 5772, 420, 32, 9, 1

Offset

0,4

Comments

Row sums are {1, 2, 7, 24, 99, 702, 6133, 54116, 559453, 7202238, ...}.

Links

Table of n, a(n) for n=0..54.

Formula

t(n,q) = If[n == 0, 1, Sum[Eulerian[n, k]*q^n, {k, 1, n, 2}]].

Example

{1},
{1, 1},
{4, 2, 1},
{12, 8, 3, 1},
{52, 30, 12, 4, 1},
{360, 260, 60, 16, 5, 1},
{2656, 2562, 780, 108, 20, 6, 1},
{20160, 23408, 8568, 1768, 180, 24, 7, 1},
{177472, 262950, 94752, 20580, 3380, 282, 28, 8, 1},
{1814400, 3594620, 1467840, 277984, 41160, 5772, 420, 32, 9, 1}

Mathematica

Clear[t, n, q, a]
<< DiscreteMath`Combinatorica`
t[n_, q_] = If[n == 0, 1, Sum[Eulerian[n + 1, k]*q^k, {k, 1, n, 2}]];
a = Table[Table[t[n, q], {n, 0, 10}], {q, 1, 11}];
Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
Flatten[%]

Crossrefs

Sequence in context: A049429 A328647 A183158 * A152818 A302235 A242861

Adjacent sequences: A174002 A174003 A174004 * A174006 A174007 A174008

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 05 2010

Status

approved