A058403 Coefficient triangle of polynomials (rising powers) related to Pell number convolutions. Companion triangle is A058402.

2, 20, 8, 360, 288, 48, 9840, 11360, 3520, 320, 363360, 522752, 225344, 37888, 2176, 16776000, 27849600, 14871296, 3491072, 373504, 14848, 922158720, 1692808704, 1053556480, 308703232, 46459904, 3467264, 101376, 58499239680, 115821927936

Offset

0,1

Comments

The row polynomials are q(k,x) := sum(a(k,m)*x^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^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A058402(k,m).

Links

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

W. Lang, First 7 rows, also for A058402.

Formula

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

Example

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

Crossrefs

Cf. A000129, A054456, A058402, A058404-5 (falling powers).

Sequence in context: A344545 A076495 A308387 * A083297 A343927 A221921

Adjacent sequences: A058400 A058401 A058402 * A058404 A058405 A058406

Keyword

nonn,tabl

Author

Wolfdieter Lang, Dec 11 2000

Extensions

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

Status

approved