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A061189 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000204(n+1), n >= 0 (Lucas numbers). 2
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
sign,tabl
AUTHOR
Wolfdieter Lang, Apr 20 2001
STATUS
approved

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)