A153190 Triangle read by rows: t(n,m)=If[m == 0, 1, Product[m*k + 2, {k, 0, n}]].

1, 2, 6, 2, 8, 48, 2, 10, 80, 880, 2, 12, 120, 1680, 30240, 2, 14, 168, 2856, 62832, 1696464, 2, 16, 224, 4480, 116480, 3727360, 141639680, 2, 18, 288, 6624, 198720, 7352640, 323516160, 16499324160, 2, 20, 360, 9360, 318240, 13366080, 668304000

Offset

0,2

Comments

Row sums are 1, 8, 58, 972, 32054, 1762336, 145488242, 16830398612, 2597711342062, 515721781568424, 128010625761216554, ....

Links

Table of n, a(n) for n=0..42.

Formula

t(n,m)=If[m == 0, 1, Product[m*k + 2, {k, 0, n}]]. t(n,m)=m^(1+n)*Pochhammer[2/m,n+1].

Example

{1},
{2, 6},
{2, 8, 48},
{2, 10, 80, 880},
{2, 12, 120, 1680, 30240},
{2, 14, 168, 2856, 62832, 1696464},
{2, 16, 224, 4480, 116480, 3727360, 141639680},
{2, 18, 288, 6624, 198720, 7352640, 323516160, 16499324160},
{2, 20, 360, 9360, 318240, 13366080, 668304000, 38761632000, 2558267712000},
{2, 22, 440, 12760, 484880, 22789360, 1276204160, 82953270400, 6138542009600, 509498986796800},
{2, 24, 528, 16896, 709632, 36900864, 2287853568, 164725456896, 13507487465472, 1242688846823424, 126754262375989248}

Mathematica

t[n_, m_] =If[m == 0, 1, Product[m*k + 2, {k, 0, n}]];
Table[Table[t[n, m], {n, 0, m}], {m, 1, 10}];
Flatten[%]

Crossrefs

Cf. A000142, A008544, A001813, A000165.

Sequence in context: A365260 A368522 A033641 * A010240 A369994 A199154

Adjacent sequences: A153187 A153188 A153189 * A153191 A153192 A153193

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 20 2008

Status

approved