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A249266
Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} x^k = Sum_{k=0..n} A_k*(x+2*(-1)^k)^k.
0
1, 3, 1, -9, -3, 1, -97, -39, 7, 1, 815, 313, -65, -7, 1, 12367, 4873, -945, -127, 11, 1, -164465, -64439, 12735, 1633, -169, -11, 1, -3314673, -1302263, 255327, 33553, -3249, -263, 15, 1, 60873999, 23899401, -4695969, -613359, 60591, 4665, -321, -15, 1
OFFSET
0,2
COMMENTS
Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x+2)^0 + A_1*(x-2)^1 + A_2*(x+2)^2 + A_3*(x-2)^3 + ... + A_n*(x+2*(-1)^n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
FORMULA
T(n,n-1) = 1-2*n*(-1)^n, for n > 0.
EXAMPLE
1;
3, 1;
-9, -3, 1;
-97, -39, 7, 1;
815, 313, -65, -7, 1;
12367, 4873, -945, -127, 11, 1;
-164465, -64439, 12735, 1633, -169, -11, 1;
-3314673, -1302263, 255327, 33553, -3249, -263, 15, 1;
60873999, 23899401, -4695969, -613359, 60591, 4665, -321, -15, 1;
PROG
(PARI) a(n, j, L)=if(j==n, return(1)); if(j!=n, return(1-sum(i=1, n-j, (-L)^i*(-1)^(i*j)*binomial(i+j, i)*a(n, i+j, L))))
for(n=0, 10, for(j=0, n, print1(a(n, j, 2), ", ")))
CROSSREFS
Cf. A248975.
Sequence in context: A019736 A213595 A140303 * A309057 A246269 A328475
KEYWORD
sign,tabl
AUTHOR
Derek Orr, Oct 23 2014
STATUS
approved