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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)).

%I A171229 #16 Nov 30 2014 09:34:36
%S A171229 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,
%T A171229 1,10,532,3926,3926,532,10,1,1,5,739,14833,40321,14833,739,5,1,1,2,
%U A171229 701,38248,282612,282612,38248,701,2,1,1,1,448,66464,1334961,3628801
%N 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)).
%C A171229 Row sums are: {1, 2, 5, 12, 45, 216, 1281, 8938, 71477, 643128, 6432551,...}.
%H A171229 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, 2009, see page 695.
%e A171229 {1},
%e A171229 {1, 1},
%e A171229 {1, 3, 1},
%e A171229 {1, 5, 5, 1},
%e A171229 {1, 9, 25, 9, 1},
%e A171229 {1, 13, 94, 94, 13, 1},
%e A171229 {1, 14, 265, 721, 265, 14, 1},
%e A171229 {1, 10, 532, 3926, 3926, 532, 10, 1},
%e A171229 {1, 5, 739, 14833, 40321, 14833, 739, 5, 1},
%e A171229 {1, 2, 701, 38248, 282612, 282612, 38248, 701, 2, 1},
%e A171229 {1, 1, 448, 66464, 1334961, 3628801, 1334961, 66464, 448, 1, 1}
%p A171229 T:= proc(n,k) if n=0 then 1 else 1 + floor(n!*exp(-(k-floor(n)/2)^2)) fi end proc:
%p A171229 for n from 0 to 20 do
%p A171229 seq(T(n,k),k=0..n)
%p A171229 od; # _Robert Israel_, Nov 30 2014
%t A171229 t[n_, k_] = If[n == 0, 1, 1 + Floor[n!*Exp[ -(k - Floor[n]/2)^2]]]
%t A171229 a = Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}]
%t A171229 Flatten[a]
%Y A171229 Cf. A008292
%K A171229 nonn,tabl
%O A171229 0,5
%A A171229 _Roger L. Bagula_, Dec 05 2009
%E A171229 Edited by _Joerg Arndt_, Nov 29 2014