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.

1, -2, 1, -2, -11, 1, -2, 70, -26, 1, -2, -362, 406, -47, 1, -2, 1663, -4994, 1303, -74, 1, -2, -7085, 53326, -27857, 3166, -107, 1, -2, 28636, -518210, 507958, -102674, 6508, -146, 1, -2, -111332, 4707262, -8310026, 2800366, -295892, 11950, -191, 1, -2, 420109, -40642370, 125613106, -67743506, 11185858, -722882, 20221, -242, 1

Offset: 0

Author

Derek Orr, Oct 18 2014

Keywords

• sign
• tabl

Comments

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.

Examples

			1;
-2,       1;
-2,     -11,       1;
-2,      70,     -26,        1;
-2,    -362,     406,      -47,       1;
-2,    1663,   -4994,     1303,     -74,       1;
-2,   -7085,   53326,   -27857,    3166,    -107,     1;
-2,   28636, -518210,   507958, -102674,    6508,  -146,    1;
-2, -111332, 4707262, -8310026, 2800366, -295892, 11950, -191, 1;
		

Crossrefs

Cf. A248811, A248829, A248826.

Programs

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, ", "))))

Formula

T(n,n-1) = 1 - 3n^2 for n > 0.