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A246788 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x+2)^k.

%I A246788 #14 Nov 21 2014 02:21:28
%S A246788 1,-3,2,9,-10,3,-23,38,-21,4,57,-122,99,-36,5,-135,358,-381,204,-55,6,
%T A246788 313,-986,1299,-916,365,-78,7,-711,2598,-4077,3564,-1875,594,-105,8,
%U A246788 1593,-6618,12051,-12564,8205,-3438,903,-136,9,-3527,16422,-34029,41196,-32115,16722,-5817,1304,-171,10
%N A246788 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x+2)^k.
%C A246788 Consider the transformation 1 + 2x + 3x^2 + 4x^3 + ... + (n+1)*x^n = A_0*(x+2)^0 + A_1*(x+2)^1 + A_2*(x+2)^2 + ... + A_n*(x+2)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
%F A246788 T(n,0) = ((6*n+8)*(-2)^n+1)/9, for n >= 0.
%F A246788 T(n,n-1) = -n*(2*n+1), for n >= 1.
%F A246788 Row n sums to A001057(n+1).
%e A246788 1;
%e A246788 -3,        2;
%e A246788 9,       -10,      3;
%e A246788 -23,      38,    -21,      4;
%e A246788 57,     -122,     99,    -36,      5;
%e A246788 -135,    358,   -381,    204,    -55,     6;
%e A246788 313,    -986,   1299,   -916,    365,   -78,     7;
%e A246788 -711,   2598,  -4077,   3564,  -1875,   594,  -105,    8;
%e A246788 1593,  -6618,  12051, -12564,   8205, -3438,   903, -136,    9;
%e A246788 -3527, 16422, -34029,  41196, -32115, 16722, -5817, 1304, -171, 10;
%o A246788 (PARI) T(n,k) = (k+1)*sum(i=0,n-k,(-2)^i*binomial(i+k+1,k+1))
%o A246788 for(n=0,10,for(k=0,n,print1(T(n,k),", ")))
%Y A246788 Cf. A248345, A045883, A014105, A001057.
%K A246788 sign,tabl
%O A246788 0,2
%A A246788 _Derek Orr_, Nov 15 2014