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A154987 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). 0
-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; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{-2, 8, 46, 220, 1166, 7168, 50878, 410996, 3726430, 37483576, 414292238,...}

LINKS

Table of n, a(n) for n=0..41.

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).

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}

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[%]

CROSSREFS

Sequence in context: A086915 A059927 A290437 * A089419 A263023 A193848

Adjacent sequences:  A154984 A154985 A154986 * A154988 A154989 A154990

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified February 25 20:58 EST 2018. Contains 299656 sequences. (Running on oeis4.)