A125231 - OEIS

%I #13 Nov 09 2019 02:02:56

%S 1,1,1,1,2,2,1,3,6,2,1,4,12,8,3,1,5,20,20,15,3,1,6,30,40,45,18,4,1,7,

%T 42,70,105,63,28,4,1,8,56,112,210,168,112,32,5,1,9,72,168,378,378,336,

%U 144,45,5,1,10,90,240,630,756,840,480,225,50,6,1,11,110,330,990,1386,1848

%N Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).

%C Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, 320, ...).

%C A125230 is another triangle with row sums = A045623.

%e First few rows of the triangle:

%e   1;

%e   1,   1;

%e   1,   2,   2;

%e   1,   3,   6,   2;

%e   1,   4,  12,   8,   3;

%e   1,   5,  20,  20,  15,   3;

%e   1,   6,  30,  40,  45,  18,   4;

%e   1,   7,  42,  70, 105,  63,  28,   4;

%e   ...

%p T:=(n,k)->ceil((k+1)/2)*binomial(n,k): for n from 0 to 12 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

%t Flatten[Table[Ceiling[(k+1)/2]Binomial[n,k],{n,0,20},{k,0,n}]] (* _Harvey P. Dale_, Aug 31 2015 *)

%Y Cf. A045623, A125230.

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Nov 24 2006

%E Edited by _N. J. A. Sloane_, Dec 02 2006