A062134 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).

1, 2, 0, 8, 24, 16, 336, 832, 576, 128, 12480, 28480, 23680, 8960, 1280, 481920, 1208832, 1167360, 552960, 130560, 12288, 22786560, 61834752, 65709056, 35911680, 10895360, 1763328, 118784, 1280885760, 3645444096

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..29.

Example

{1}; {2,0}; {8,24,16}; {336,832,576,128}; ...
pPL1(1,n)=1+2*n; pL2(1,n)=2; PL(1; n)= A054459(n)=((1+2*n)*PL(n+1)+PL(n))/4.

Crossrefs

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

Sequence in context: A308536 A241682 A076687 * A002909 A118437 A134185

Adjacent sequences: A062131 A062132 A062133 * A062135 A062136 A062137

Keyword

nonn,tabl

Author

Wolfdieter Lang, Jun 19 2001

Status

approved