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A062134 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers). 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 02:19 EDT 2020. Contains 337164 sequences. (Running on oeis4.)