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A155451 Triangle read by rows: T(n,m)=2*Binomial[n, m] - (m! - n! + (-m + n)!). 0

%I

%S 1,1,1,1,4,1,1,9,9,1,1,25,32,25,1,1,105,132,132,105,1,1,611,724,748,

%T 724,611,1,1,4333,4960,5080,5080,4960,4333,1,1,35295,39654,40306,

%U 40412,40306,39654,35295,1,1,322577,357910,362322,362988,362988,362322,357910

%N Triangle read by rows: T(n,m)=2*Binomial[n, m] - (m! - n! + (-m + n)!).

%C Row sums are: {1, 2, 6, 20, 84, 476, 3420, 28748, 270924, 2811596, 31843020,...}.

%F T(n,m)=2*Binomial[n, m] - (m! - n! + (-m + n)!).

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 9, 9, 1},

%e {1, 25, 32, 25, 1},

%e {1, 105, 132, 132, 105, 1},

%e {1, 611, 724, 748, 724, 611, 1},

%e {1, 4333, 4960, 5080, 5080, 4960, 4333, 1},

%e {1, 35295, 39654, 40306, 40412, 40306, 39654, 35295, 1},

%e {1, 322577, 357910, 362322, 362988, 362988, 362322, 357910, 322577, 1},

%e {1, 3265939, 3588568, 3623994, 3628476, 3629064, 3628476, 3623994, 3588568, 3265939, 1}

%t Table[Table[ 2*Binomial[n, m] - (m! - n! + (-m + n)!), {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Jan 22 2009

%E Edited by _N. J. A. Sloane_, Jan 25 2009

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Last modified July 31 02:16 EDT 2021. Contains 346367 sequences. (Running on oeis4.)