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

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, 724, 611, 1, 1, 4333, 4960, 5080, 5080, 4960, 4333, 1, 1, 35295, 39654, 40306, 40412, 40306, 39654, 35295, 1, 1, 322577, 357910, 362322, 362988, 362988, 362322, 357910

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..52.

Formula

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

Example

{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, 724, 611, 1},
{1, 4333, 4960, 5080, 5080, 4960, 4333, 1},
{1, 35295, 39654, 40306, 40412, 40306, 39654, 35295, 1},
{1, 322577, 357910, 362322, 362988, 362988, 362322, 357910, 322577, 1},
{1, 3265939, 3588568, 3623994, 3628476, 3629064, 3628476, 3623994, 3588568, 3265939, 1}

Mathematica

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

Crossrefs

Sequence in context: A347972 A146767 A146955 * A220681 A189280 A168621

Adjacent sequences: A155448 A155449 A155450 * A155452 A155453 A155454

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 22 2009

Extensions

Edited by N. J. A. Sloane, Jan 25 2009

Status

approved