A058405 Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058404.

2, 8, 20, 48, 288, 360, 320, 3520, 11360, 9840, 2176, 37888, 225344, 522752, 363360, 14848, 373504, 3491072, 14871296, 27849600, 16776000, 101376, 3467264, 46459904, 308703232, 1053556480, 1692808704, 922158720, 692224, 30834688

Offset

0,1

Comments

The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..

The k-th convolution of P0(n) := A000129(n+1), n >= 0, (Pell numbers starting with P0(0)=1) with itself is Pk(n) := A054456(n+k,k) = (p(k-1,n)*(n+1)*2*P0(n+1) + q(k-1,n)*(n+2)*P0(n))/(k!*8^k), k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A058404(k,m).

Links

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

W. Lang, First 7 rows, also for A058404.

Formula

Recursion for row polynomials defined in the comments: see A058402.

Example

k=2: P2(n)=((8*n+22)*(n+1)*2*P0(n+1)+(8*n+20)*(n+2)*P0(n))/128, cf. A054457.
2; 8,20; 48,288,360; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0)

Crossrefs

Cf. A000129, A054456, A058404, A054457, A058402-3 (rising powers).

Sequence in context: A240940 A066857 A146168 * A133326 A285185 A302323

Adjacent sequences: A058402 A058403 A058404 * A058406 A058407 A058408

Keyword

nonn,tabl

Author

Wolfdieter Lang, Dec 11 2000

Extensions

Link and cross-references added by Wolfdieter Lang, Jul 31 2002

Status

approved