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A246797 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 A246797 #17 Nov 22 2014 03:48:46
%S A246797 1,5,2,17,14,3,49,62,27,4,129,222,147,44,5,321,702,627,284,65,6,769,
%T A246797 2046,2307,1404,485,90,7,1793,5630,7683,5884,2725,762,119,8,4097,
%U A246797 14846,23811,22012,12805,4794,1127,152,9,9217,37886,69891,75772,53125,24954,7847,1592,189,10
%N A246797 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 A246797 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 A246797 T(n,0) = n*2^(n+1)+1, for n >= 0.
%F A246797 T(n,n-1) = n*(2*n+3), for n >= 1.
%F A246797 Row n sums to A014915(n-1) = T(n,0) of A246799.
%e A246797 Triangle starts:
%e A246797 1;
%e A246797 5,        2;
%e A246797 17,      14,     3;
%e A246797 49,      62,    27,     4;
%e A246797 129,    222,   147,    44,     5;
%e A246797 321,    702,   627,   284,    65,     6;
%e A246797 769,   2046,  2307,  1404,   485,    90,    7;
%e A246797 1793,  5630,  7683,  5884,  2725,   762,  119,    8;
%e A246797 4097, 14846, 23811, 22012, 12805,  4794, 1127,  152,   9;
%e A246797 9217, 37886, 69891, 75772, 53125, 24954, 7847, 1592, 189, 10;
%e A246797 ...
%o A246797 (PARI) T(n,k) = (k+1)*sum(i=0,n-k,2^i*binomial(i+k+1,k+1))
%o A246797 for(n=0,10,for(k=0,n,print1(T(n,k),", ")))
%Y A246797 Cf. A246788, A014106, A000337, A246799.
%K A246797 nonn,tabl
%O A246797 0,2
%A A246797 _Derek Orr_, Nov 15 2014