login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062133 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers). 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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