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A248977 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + ... + x^n to the polynomial A_k*(x+3k)^k for 0 <= k <= n.

%I A248977 #8 Oct 23 2014 20:51:32
%S A248977 1,-2,1,-2,-11,1,-2,70,-26,1,-2,-362,406,-47,1,-2,1663,-4994,1303,-74,
%T A248977 1,-2,-7085,53326,-27857,3166,-107,1,-2,28636,-518210,507958,-102674,
%U A248977 6508,-146,1,-2,-111332,4707262,-8310026,2800366,-295892,11950,-191,1,-2,420109,-40642370,125613106,-67743506,11185858,-722882,20221,-242,1
%N A248977 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + ... + x^n to the polynomial A_k*(x+3k)^k for 0 <= k <= n.
%C A248977 Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x+0)^0 + A_1*(x+3)^1 + A_2*(x+6)^2 + ... + A_n*(x+3n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
%F A248977 T(n,n-1) = 1 - 3n^2 for n > 0.
%e A248977 1;
%e A248977 -2,       1;
%e A248977 -2,     -11,       1;
%e A248977 -2,      70,     -26,        1;
%e A248977 -2,    -362,     406,      -47,       1;
%e A248977 -2,    1663,   -4994,     1303,     -74,       1;
%e A248977 -2,   -7085,   53326,   -27857,    3166,    -107,     1;
%e A248977 -2,   28636, -518210,   507958, -102674,    6508,  -146,    1;
%e A248977 -2, -111332, 4707262, -8310026, 2800366, -295892, 11950, -191, 1;
%o A248977 (PARI) for(n=0, 10, for(k=0, n, if(!k, if(n, print1(-2, ", ")); if(!n, print1(1, ", "))); if(k, print1(sum(i=1, n, ((-3*k)^(i-k)*i*binomial(i,k)))/k, ", "))))
%Y A248977 Cf. A248811, A248829, A248826.
%K A248977 sign,tabl
%O A248977 0,2
%A A248977 _Derek Orr_, Oct 18 2014