A248977 - OEIS

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

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OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

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

EXAMPLE

-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;

PROG

(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, ", "))))

CROSSREFS

Cf. A248811, A248829, A248826.

Sequence in context: A062345 A077098 A069238 * A266655 A209610 A324058

Adjacent sequences: A248974 A248975 A248976 * A248978 A248979 A248980

KEYWORD

sign,tabl

AUTHOR

Derek Orr, Oct 18 2014

STATUS

approved