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A154987
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Triangle read by rows: t1(n,m) = 2*n!*Gamma[n + 1/2 + m]/(Gamma[n - 1/2 + m]*m!); t(n,m)=t1(n,m)+t1(n,n-m).
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0
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-2, 4, 4, 13, 20, 13, 41, 69, 69, 41, 183, 268, 264, 268, 183, 1099, 1405, 1080, 1080, 1405, 1099, 7943, 9486, 5970, 4080, 5970, 9486, 7943, 65547, 75775, 43806, 20370, 20370, 43806, 75775, 65547, 604831, 685672, 384552, 149520, 77280, 149520
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{-2, 8, 46, 220, 1166, 7168, 50878, 410996, 3726430, 37483576, 414292238,...}
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FORMULA
| t1(n,m) = 2*n!*Gamma[n + 1/2 + m]/(Gamma[n - 1/2 + m]*m!);
t(n,m)=t1(n,m)+t1(n,n-m).
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EXAMPLE
| {-2},
{4, 4},
{13, 20, 13},
{41, 69, 69, 41},
{183, 268, 264, 268, 183},
{1099, 1405, 1080, 1080, 1405, 1099},
{7943, 9486, 5970, 4080, 5970, 9486, 7943},
{65547, 75775, 43806, 20370, 20370, 43806, 75775, 65547},
{604831, 685672, 384552, 149520, 77280, 149520, 384552, 685672, 604831},
{6168995, 6895017, 3812472, 1405656, 459648, 459648, 1405656, 3812472, 6895017, 6168995},
{68947239, 76205170, 41734350, 15143760, 4238640, 1753920, 4238640, 15143760, 41734350, 76205170, 68947239}
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MATHEMATICA
| Clear[t, t1, n, m, a];
t1[n_, m_] = 2*n!*Gamma[n + 1/2 + m]/(Gamma[n - 1/2 + m]*m!);
t[n_, m_] = t1[n, m] + t1[n, n - m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A129017 A086915 A059927 * A089419 A193848 A145891
Adjacent sequences: A154984 A154985 A154986 * A154988 A154989 A154990
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 18 2009
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