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 A125102 Triangle read by rows: T(n,k)=(k+1)binomial(n,k) + [3-(-1)^k]binomial(n,k+1)/2 (0<=k<=n). 0

%I

%S 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,

%T 7,8,56,98,210,196,140,50,8,9,72,140,364,406,392,204,66,9,10,90,192,

%U 588,756,924,624,306,82,10,11,110,255,900,1302,1932,1590,1050,415,102,11,12

%N Triangle read by rows: T(n,k)=(k+1)binomial(n,k) + [3-(-1)^k]binomial(n,k+1)/2 (0<=k<=n).

%C 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 First few rows of the triangle are:

%e 1;

%e 2, 2;

%e 3, 6, 3;

%e 4, 12, 10, 4;

%e 5, 20, 22, 18, 5;

%e 6, 30, 40, 50, 26, 6;

%e 7, 42, 65, 110, 81, 38, 7;

%e ...

%p 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

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Nov 20 2006

%E Edited by _N. J. A. Sloane_, Nov 29 2006

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)