%I A125102
%S A125102 1,2,2,3,6,3,4,12,10,4,5,20,22,18,5,6,30,40,50,26,6,7,42,65,110,81,38,
               7,
%T A125102 8,56,98,210,196,140,50,8,9,72,140,364,406,392,204,66,9,10,90,192,588,
%U A125102 756,924,624,306,82,10,11,110,255,900,1302,1932,1590,1050,415,102,11,12
%N A125102 Triangle read by rows: T(n,k)=(k+1)binomial(n,k) + [3-(-1)^k]binomial(n,
               k+1)/2 (0<=k<=n).
%C A125102 Binomial transform of the bidiagonal matrix with (1,2,3...) in the main 
               diagonal and (1,2,1,2,1,2...) in the subdiagonal. Sum of terms in 
               row n = (n+5)*2^(n-1)-2 for n>=1.
%e A125102 First few rows of the triangle are:
%e A125102 1;
%e A125102 2, 2;
%e A125102 3, 6, 3;
%e A125102 4, 12, 10, 4;
%e A125102 5, 20, 22, 18, 5;
%e A125102 6, 30, 40, 50, 26, 6;
%e A125102 7, 42, 65, 110, 81, 38, 7;
%e A125102 ...
%p A125102 T:=(n,k)->(k+1)*binomial(n,k)+(3-(-1)^k)*binomial(n,k+1)/2: for n from 
               0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular 
               form
%Y A125102 Sequence in context: A064426 A051173 A128228 this_sequence A003506 A047662 
               A075196
%Y A125102 Adjacent sequences: A125099 A125100 A125101 this_sequence A125103 A125104 
               A125105
%K A125102 nonn,tabl
%O A125102 0,2
%A A125102 Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 20 2006
%E A125102 Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006