%I #21 Sep 08 2022 08:45:49

%S 1,1,1,1,2,1,1,3,3,1,1,7,13,7,1,1,13,51,51,13,1,1,23,181,361,181,23,1,

%T 1,34,530,2120,2120,530,34,1,1,40,1261,10081,20161,10081,1261,40,1,1,

%U 38,2384,38144,152573,152573,38144,2384,38,1

%N Triangle read by rows: T(n,k) = 1 + floor(n!/2^((k - n/2)^2 + 1)).

%H G. C. Greubel, <a href="/A171246/b171246.txt">Rows n = 0..100 of triangle, flattened</a>

%H Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, page 695.

%F T(n,k) = 1 + floor(n!/2^((k - n/2)^2 +1)).

%e Triangle begins as:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 3, 3, 1;

%e 1, 7, 13, 7, 1;

%e 1, 13, 51, 51, 13, 1;

%e 1, 23, 181, 361, 181, 23, 1;

%e 1, 34, 530, 2120, 2120, 530, 34, 1;

%t T[n_, k_]:= 1 +Floor[n!*2^(-(k-n/2)^2 -1)]; Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten

%o (PARI) {T(n,k) = 1 + floor(n!/2^((k - n/2)^2 +1))}; \\ _G. C. Greubel_, Apr 11 2019

%o (Magma) [[1 +Floor(Factorial(n)/2^((k - n/2)^2 +1)): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, Apr 11 2019

%o (Sage) [[1 + floor(factorial(n)/2^((k-n/2)^2 +1)) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Apr 11 2019

%Y Cf. A171229.

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Dec 06 2009

%E Edited by _G. C. Greubel_, Apr 11 2019