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A174696 A symmetrical triangle sequence: t(n,m)=n!*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2 - n! + 1 0
1, 1, 1, 1, 49, 1, 1, 841, 841, 1, 1, 11881, 47881, 11881, 1, 1, 161281, 1799281, 1799281, 161281, 1, 1, 2217601, 55560961, 154344961, 55560961, 2217601, 1, 1, 31570561, 1548892801, 9680791681, 9680791681, 1548892801, 31570561, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 51, 1684, 71645, 3921126, 269902087, 22522510088, 2215754352009,

251470650816010,...}.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

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

EXAMPLE

{1},

{1, 1},

{1, 49, 1},

{1, 841, 841, 1},

{1, 11881, 47881, 11881, 1},

{1, 161281, 1799281, 1799281, 161281, 1},

{1, 2217601, 55560961, 154344961, 55560961, 2217601, 1},

{1, 31570561, 1548892801, 9680791681, 9680791681, 1548892801, 31570561, 1},

{1, 469929601, 40967337601, 501853968001, 1129171881601, 501853968001, 40967337601, 469929601, 1},

{1, 7344691201, 1058154451201, 23044327891201, 101625498374401, 101625498374401, 23044327891201, 1058154451201, 7344691201, 1}

MATHEMATICA

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

Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A115480 A214953 A005071 * A203506 A254617 A012120

Adjacent sequences:  A174693 A174694 A174695 * A174697 A174698 A174699

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 27 2010

STATUS

approved

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Last modified December 13 19:20 EST 2017. Contains 295976 sequences.