login
Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).
3

%I #4 Mar 31 2012 13:20:05

%S 1,2,0,8,24,16,336,832,576,128,12480,28480,23680,8960,1280,481920,

%T 1208832,1167360,552960,130560,12288,22786560,61834752,65709056,

%U 35911680,10895360,1763328,118784,1280885760,3645444096

%N Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).

%C The row polynomials pPL1(n,x) := sum(A062133(n,m)*x^m,m=0..n) and pPL2(n,x) := sum(a(n,m)*x^m,m=0..n) appear in the k-fold convolution of the associated Pell numbers PL(n) := A001333(n+1), n >= 0, as follows: PL(k; n) := A054458(n+k,k)= (2*pPL1(k,n)*PL(n+1)+pPL2(k,n)*PL(n)/(k!*8^k), k >= 0.

%e {1}; {2,0}; {8,24,16}; {336,832,576,128}; ...

%e pPL1(1,n)=1+2*n; pL2(1,n)=2; PL(1; n)= A054459(n)=((1+2*n)*PL(n+1)+PL(n))/4.

%Y A062133(n, m) (companion triangle), A054458(n, m) (convolution triangle).

%K nonn,tabl

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001