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A176063
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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]
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0
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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
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OFFSET
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0,5
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COMMENTS
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Row sums are:
{1, 7, 43, 297, 2371, 21613, 221523, 2520577, 31515427, 429407661,...}.
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LINKS
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FORMULA
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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]
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EXAMPLE
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{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}
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MATHEMATICA
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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[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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