A061189 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000204(n+1), n >= 0 (Lucas numbers).

1, 2, 0, -10, 15, 25, 30, 475, 450, 125, 6000, 8500, 6250, 5000, 1250, 96000, 146250, 189375, 159375, 65625, 9375, 180000, 5355000, 8881250, 5578125, 2515625, 721875, 78125, 44100000, 254700000, 341775000

Offset

0,2

Comments

The row polynomials pL2(n,x) := sum(a(n,m)*x^m,m=0..n) and pL1(n,x) := sum(A061188(n,m)*x^m,m=0..n) appear in the k-fold convolution of the Lucas numbers L(n+1)= A000204(n+1)= A000032(n+1), n >= 0, as follows: L(k; n) := A060922(n+k,k)= (pL1(k,n)*L(n+2)+pL2(k,n)*L(n+1)/(k!*5^k).

Links

Table of n, a(n) for n=0..30.

Example

{1}; {2,0}; {-10,15,25}; {30,475,450,125}; ...; pL2(2,n)=5*(-2+3*n+5*n^2)= 5*(1+n)*(-2+5*n).
L(2; n) := A060922(n+2,2)= A060929(n) = (1+n)*((4+5*n)*L(n+2)+(-2+5*n)*L(n+1))/(2*5).

Crossrefs

A061188(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).

Sequence in context: A351879 A070681 A228539 * A019220 A019140 A361816

Adjacent sequences: A061186 A061187 A061188 * A061190 A061191 A061192

Keyword

sign,tabl

Author

Wolfdieter Lang, Apr 20 2001

Status

approved