A062133 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).

0, 1, 2, 20, 36, 16, 456, 944, 672, 160, 14304, 33760, 28800, 10880, 1536, 575040, 1466752, 1413120, 666880, 157440, 14848, 27659520, 74774784, 79278080, 43330560, 13153280, 2128896, 143360, 1548126720

Offset

0,3

Comments

The row polynomials pPL1(n,x) := sum(a(n,m)*x^m,m=0..n) and pPL2(n,x) := sum(A062134(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..28.

Example

{0}; {1,2}; {20,36,16}; {456,944,672,160}; ...
pPL1(2,n)=4*(5+9*n+4*n^2)=4*(1+n)*(5+4*n); pL2(2,n)=8*(1+3*n+2*n^2)=8*(1+n)*(1+2*n); PL(2; n)= A054460(n)=(1+n)*((5+4*n)*PL(n+1)+(1+2*n)*PL(n))/16.

Crossrefs

A062134(n, m) (companion triangle), A054458(n, m) (convolution triangle).

Sequence in context: A103076 A293029 A298761 * A329729 A050684 A073214

Adjacent sequences: A062130 A062131 A062132 * A062134 A062135 A062136

Keyword

nonn,tabl

Author

Wolfdieter Lang, Jun 19 2001

Status

approved