|
%I #20 Jul 22 2015 08:35:05
%S 1,2,2,4,4,3,8,14,6,4,16,40,36,8,5,32,122,120,76,10,6,64,364,528,272,
%T 140,12,7,128,1094,2016,1684,520,234,14,8,256,3280,8256,7448,4400,888,
%U 364,16,9,512,9842,32640,40156,21280,9966,1400,536,18,10
%N Array T(n,k) read by antidiagonals: T(n,k) = Sum_{v=1..n, v odd} binomial(n,v)*k^v.
%C Antidiagonal sums are: 1, 4, 11, 32, 105, 366, 1387, ...
%e 1, 2, 3, 4, 5, 6, 7, ...
%e 2, 4, 6, 8, 10, 12, 14, ...
%e 4, 14, 36, 76, 140, 234, 364, ...
%e 8, 40, 120, 272, 520, 888, 1400, ...
%e 16, 122, 528, 1684, 4400, 9966, 20272, ...
%e 32, 364, 2016, 7448, 21280, 51012, 107744, ...
%e 64, 1094, 8256, 40156, 148160, 450834, 1188544, ...
%o (PARI) tabl(nn) = {for (n=1, nn, for (k=1, nn, print1(sum(v=1, n, (v%2)*binomial(n, v)*k^v), ", ");); print(););} \\ _Michel Marcus_, Jul 22 2015
%Y Cf. A152011.
%Y Cf. A005843 (2nd line), A079908 (3rd line), A105374 (4th line).
%K nonn,tabl
%O 1,2
%A _Roger L. Bagula_, Mar 03 2010
|
