A246798 - OEIS

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A246798

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+3)^k.

1, -5, 2, 22, -16, 3, -86, 92, -33, 4, 319, -448, 237, -56, 5, -1139, 1982, -1383, 484, -85, 6, 3964, -8224, 7122, -3296, 860, -120, 7, -13532, 32600, -33702, 19384, -6700, 1392, -161, 8, 45517, -124864, 150006, -103088, 44330, -12216, 2107, -208, 9, -151313, 465626, -637314, 509272, -261850, 89844, -20573, 3032, -261, 10

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OFFSET

0,2

COMMENTS

Consider the transformation 1 + 2x + 3x^2 + 4x^3 + ... + (n+1)*x^n = A_0*(x+3)^0 + A_1*(x+3)^1 + A_2*(x+3)^2 + ... + A_n*(x+3)^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,0) = (1-(4*n+5)*(-3)^(n+1))/16, for n >= 0.

T(n,n-1) = -n*(3*n+2), for n >= 1.

Row n sums to (-1)^n*A045883(n+1) = T(n,0) of A246788.

EXAMPLE

Triangle starts:

-5, 2;

22, -16, 3;

-86, 92, -33, 4;

319, -448, 237, -56, 5;

-1139, 1982, -1383, 484, -85, 6;

3964, -8224, 7122, -3296, 860, -120, 7;

-13532, 32600, -33702, 19384, -6700, 1392, -161, 8;

45517, -124864, 150006, -103088, 44330, -12216, 2107, -208, 9;

-151313, 465626, -637314, 509272, -261850, 89844, -20573, 3032, -261, 10;

...

PROG

(PARI) T(n, k) = (k+1)*sum(i=0, n-k, (-3)^i*binomial(i+k+1, k+1))

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")))

CROSSREFS

Cf. A246788, A045944, A191008.

Sequence in context: A096035 A074769 A036165 * A367675 A372063 A230416

Adjacent sequences: A246795 A246796 A246797 * A246799 A246800 A246801

KEYWORD

sign,tabl

AUTHOR

Derek Orr, Nov 15 2014

STATUS

approved