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A155162 Triangle T(n,k) = binomial(n, k)*(k! + (n-k)!), read by rows.

%I A155162 #9 Jan 05 2024 15:00:48
%S A155162 2,2,2,3,4,3,7,9,9,7,25,28,24,28,25,121,125,80,80,125,121,721,726,390,
%T A155162 240,390,726,721,5041,5047,2562,1050,1050,2562,5047,5041,40321,40328,
%U A155162 20216,7056,3360,7056,20216,40328,40321,362881,362889,181512,60984,18144,18144,60984,181512,362889,362881
%N A155162 Triangle T(n,k) = binomial(n, k)*(k! + (n-k)!), read by rows.
%H A155162 G. C. Greubel, <a href="/A155162/b155162.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A155162 T(n,k) = binomial(n, k)*(k! + (n-k)!).
%F A155162 Sum_{k=0..n} T(n, k) = 2*A000522(n) = A054091(n+1). - _G. C. Greubel_, Mar 19 2021
%e A155162 Triangle begins as:
%e A155162        2;
%e A155162        2,      2;
%e A155162        3,      4,      3;
%e A155162        7,      9,      9,     7;
%e A155162       25,     28,     24,    28,    25;
%e A155162      121,    125,     80,    80,   125,   121;
%e A155162      721,    726,    390,   240,   390,   726,   721;
%e A155162     5041,   5047,   2562,  1050,  1050,  2562,  5047,   5041;
%e A155162    40321,  40328,  20216,  7056,  3360,  7056, 20216,  40328,  40321;
%e A155162   362881, 362889, 181512, 60984, 18144, 18144, 60984, 181512, 362889, 362881;
%p A155162 A155162:= (n,k)-> binomial(n,k)*(k! + (n-k)!); seq(seq(A155162(n,k), k=0..n), n=0..12); # _G. C. Greubel_, Mar 19 2021
%t A155162 Table[Binomial[n,k](k! +(n-k)!), {n,0,12},{k,0,n}]//Flatten
%o A155162 (Magma) [Binomial(n,k)*(Factorial(k) + Factorial(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 19 2021
%o A155162 (Sage) flatten([[binomial(n,k)*(factorial(k) + factorial(n-k)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 19 2021
%Y A155162 Cf. A000522, A054091.
%K A155162 nonn,tabl
%O A155162 0,1
%A A155162 _Roger L. Bagula_, Jan 21 2009
%E A155162 Edited by _G. C. Greubel_, Mar 19 2021