cp's OEIS Frontend

A125231 Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).

%I A125231 #13 Nov 09 2019 02:02:56
%S A125231 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 A125231 42,70,105,63,28,4,1,8,56,112,210,168,112,32,5,1,9,72,168,378,378,336,
%U A125231 144,45,5,1,10,90,240,630,756,840,480,225,50,6,1,11,110,330,990,1386,1848
%N A125231 Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).
%C A125231 Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, 320, ...).
%C A125231 A125230 is another triangle with row sums = A045623.
%e A125231 First few rows of the triangle:
%e A125231   1;
%e A125231   1,   1;
%e A125231   1,   2,   2;
%e A125231   1,   3,   6,   2;
%e A125231   1,   4,  12,   8,   3;
%e A125231   1,   5,  20,  20,  15,   3;
%e A125231   1,   6,  30,  40,  45,  18,   4;
%e A125231   1,   7,  42,  70, 105,  63,  28,   4;
%e A125231   ...
%p A125231 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 A125231 Flatten[Table[Ceiling[(k+1)/2]Binomial[n,k],{n,0,20},{k,0,n}]] (* _Harvey P. Dale_, Aug 31 2015 *)
%Y A125231 Cf. A045623, A125230.
%K A125231 nonn,tabl
%O A125231 0,5
%A A125231 _Gary W. Adamson_, Nov 24 2006
%E A125231 Edited by _N. J. A. Sloane_, Dec 02 2006