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A171246 Triangle read by rows: T(n,k) = 1 + floor(n!/2^((k - n/2)^2 + 1)).

%I A171246 #21 Sep 08 2022 08:45:49
%S A171246 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 A171246 1,34,530,2120,2120,530,34,1,1,40,1261,10081,20161,10081,1261,40,1,1,
%U A171246 38,2384,38144,152573,152573,38144,2384,38,1
%N A171246 Triangle read by rows: T(n,k) = 1 + floor(n!/2^((k - n/2)^2 + 1)).
%H A171246 G. C. Greubel, <a href="/A171246/b171246.txt">Rows n = 0..100 of triangle, flattened</a>
%H A171246 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 A171246 T(n,k) = 1 + floor(n!/2^((k - n/2)^2 +1)).
%e A171246 Triangle begins as:
%e A171246    1;
%e A171246    1,  1;
%e A171246    1,  2,   1;
%e A171246    1,  3,   3,    1;
%e A171246    1,  7,  13,    7,    1;
%e A171246    1, 13,  51,   51,   13,   1;
%e A171246    1, 23, 181,  361,  181,  23,  1;
%e A171246    1, 34, 530, 2120, 2120, 530, 34, 1;
%t A171246 T[n_, k_]:= 1 +Floor[n!*2^(-(k-n/2)^2 -1)]; Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten
%o A171246 (PARI) {T(n,k) = 1 + floor(n!/2^((k - n/2)^2 +1))}; \\ _G. C. Greubel_, Apr 11 2019
%o A171246 (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 A171246 (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 A171246 Cf. A171229.
%K A171246 nonn,tabl
%O A171246 0,5
%A A171246 _Roger L. Bagula_, Dec 06 2009
%E A171246 Edited by _G. C. Greubel_, Apr 11 2019