A061188 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000032(n+1), n >= 0 (Lucas numbers).

0, 1, 5, 20, 45, 25, 240, 350, 600, 250, 3000, 9250, 13125, 8750, 1875, 93000, 373750, 361875, 240625, 103125, 15625, 3690000, 11077500, 12818750, 8531250, 4156250, 1181250, 125000, 116550000, 312037500

Offset

0,3

Comments

The row polynomials pL1(n,x) := sum(a(n,m)*x^m,m=0..n) and pL2(n,x) := sum(A061189(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..29.

Example

{0}; {1,5}; {20,45,25}; {240,350,600,250}; ...; pL1(2,n)=5*(4+9*n+5*n^2)= 5*(1+n)*(4+5*n).

Crossrefs

A061189(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).

Sequence in context: A363695 A228168 A178977 * A033429 A168011 A160749

Adjacent sequences: A061185 A061186 A061187 * A061189 A061190 A061191

Keyword

nonn,tabl

Author

Wolfdieter Lang, Apr 20 2001

Status

approved