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A155516 Triangle read by rows: t(n,m)=(2*n + 1)!!/((2*m + 1)!!*(2*(n - m) + 1)!!)*Binomial[2*n, 2*m]*Binomial[n, m]; 0
1, 1, 1, 1, 20, 1, 1, 105, 105, 1, 1, 336, 1764, 336, 1, 1, 825, 13860, 13860, 825, 1, 1, 1716, 70785, 226512, 70785, 1716, 1, 1, 3185, 273273, 2147145, 2147145, 273273, 3185, 1, 1, 5440, 866320, 14158144, 34763300, 14158144, 866320, 5440, 1, 1, 8721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 22, 212, 2438, 29372, 371516, 4847208, 64823110, 883629164,

12233141908,...}.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

t(n,m)=(2*n + 1)!!/((2*m + 1)!!*(2*(n - m) + 1)!!)*Binomial[2*n, 2*m]*Binomial[n, m];

EXAMPLE

{1},

{1, 1},

{1, 20, 1},

{1, 105, 105, 1},

{1, 336, 1764, 336, 1},

{1, 825, 13860, 13860, 825, 1},

{1, 1716, 70785, 226512, 70785, 1716, 1},

{1, 3185, 273273, 2147145, 2147145, 273273, 3185, 1},

{1, 5440, 866320, 14158144, 34763300, 14158144, 866320, 5440, 1},

{1, 8721, 2372112, 71954064, 367479684, 367479684, 71954064, 2372112, 8721, 1},

{1, 13300, 5799465, 300467520, 2848181700, 5924217936, 2848181700, 300467520, 5799465, 13300, 1}

MATHEMATICA

Clear[t, n, m];

t[n_, m_] := (2*n + 1)!!/(( 2*m + 1)!!*(2*(n - m) + 1)!!)*Binomial[2*n, 2*m]*Binomial[n, m];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A040400 A139459 A154652 * A174674 A144443 A257608

Adjacent sequences:  A155513 A155514 A155515 * A155517 A155518 A155519

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Jan 23 2009

STATUS

approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)