A176063 Asymmetrical triangle sequence:t(n,m)=(-1)^m* Binomial[n, m] Pochhammer[ -n, m] - (-1)^n Pochhammer[ -n, n] + (-1)^( n - m)* Binomial[n, -m + n] Pochhammer[ -n, -m + n].

1, 1, 1, 1, 6, 1, 1, 21, 21, 1, 1, 88, 120, 88, 1, 1, 505, 680, 680, 505, 1, 1, 3636, 5130, 4080, 5130, 3636, 1, 1, 30289, 48762, 31710, 31710, 48762, 30289, 1, 1, 282304, 525728, 354816, 194880, 354816, 525728, 282304, 1, 1, 2903121, 6171552, 4759776

Offset: 0

Author

Roger L. Bagula, Apr 07 2010

Keywords

• nonn
• tabl
• uned

Comments

Row sums are:

{1, 7, 43, 297, 2371, 21613, 221523, 2520577, 31515427, 429407661,...}.

Examples

			{1},
{1, 1},
{1, 6, 1},
{1, 21, 21, 1},
{1, 88, 120, 88, 1},
{1, 505, 680, 680, 505, 1},
{1, 3636, 5130, 4080, 5130, 3636, 1},
{1, 30289, 48762, 31710, 31710, 48762, 30289, 1},
{1, 282304, 525728, 354816, 194880, 354816, 525728, 282304, 1},
{1, 2903121, 6171552, 4759776, 1923264, 1923264, 4759776, 6171552, 2903121, 1},
{1, 32659300, 78023250, 69033600, 29181600, 11612160, 29181600, 69033600, 78023250, 32659300, 1}
		

Crossrefs

Cf. A021010

Programs

Mathematica

L[n_, m_] = (-1)^m* Binomial[n, m] Pochhammer[ -n, m] - (-1)^n Pochhammer[ -n, n] + (-1)^(n - m)* Binomial[n, - m + n] Pochhammer[ -n, -m + n];
Table[Table[L[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

t(n,m)=(-1)^m* Binomial[n, m] Pochhammer[ -n, m] - (-1)^n Pochhammer[ -n, n] + (-1)^( n - m)* Binomial[n, -m + n] Pochhammer[ -n, -m + n]