A171229 Triangle T(n,k) read by rows: T(0,k)=1, otherwise T(n,k)= 1 + floor(n!*exp(-(k-floor(n)/2)^2)).

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 9, 25, 9, 1, 1, 13, 94, 94, 13, 1, 1, 14, 265, 721, 265, 14, 1, 1, 10, 532, 3926, 3926, 532, 10, 1, 1, 5, 739, 14833, 40321, 14833, 739, 5, 1, 1, 2, 701, 38248, 282612, 282612, 38248, 701, 2, 1, 1, 1, 448, 66464, 1334961, 3628801

Offset: 0

Author

Roger L. Bagula, Dec 05 2009

Keywords

• nonn
• tabl

Comments

Row sums are: {1, 2, 5, 12, 45, 216, 1281, 8938, 71477, 643128, 6432551,...}.

Examples

			{1},
{1, 1},
{1, 3, 1},
{1, 5, 5, 1},
{1, 9, 25, 9, 1},
{1, 13, 94, 94, 13, 1},
{1, 14, 265, 721, 265, 14, 1},
{1, 10, 532, 3926, 3926, 532, 10, 1},
{1, 5, 739, 14833, 40321, 14833, 739, 5, 1},
{1, 2, 701, 38248, 282612, 282612, 38248, 701, 2, 1},
{1, 1, 448, 66464, 1334961, 3628801, 1334961, 66464, 448, 1, 1}
		

Links

• P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009, see page 695.

Crossrefs

Cf. A008292

Programs

Maple

T:= proc(n,k) if n=0 then 1 else 1 + floor(n!*exp(-(k-floor(n)/2)^2)) fi end proc:
for n from 0 to 20 do
seq(T(n,k),k=0..n)
od; # Robert Israel, Nov 30 2014

Mathematica

t[n_, k_] = If[n == 0, 1, 1 + Floor[n!*Exp[ -(k - Floor[n]/2)^2]]]
a = Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}]
Flatten[a]

Extensions

Edited by Joerg Arndt, Nov 29 2014