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

1, 8, 22, 56, 376, 588, 384, 4576, 17024, 19656, 2624, 48256, 313504, 848096, 801360, 17920, 468608, 4643072, 21685888, 47494272, 38797920, 122368, 4307456, 60136448, 424509952, 1590913920, 2986217856, 2181332160, 835584, 38055936

Offset

0,2

Comments

The row polynomials are p(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 q(k,n) := sum(b(k,m)*n^(k-m),m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A058405(k,m).

a(k,0)= A057084(k), k >= 0 (conjecture).

Links

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

W. Lang, First 7 rows, also for A058405.

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.
1; 8,22; 56,376,588; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0)

Crossrefs

Cf. A000129, A054456, A058405, A054457, A057084, A058402-3 (rising powers).

Sequence in context: A369593 A002968 A211530 * A350123 A211479 A318034

Adjacent sequences: A058401 A058402 A058403 * A058405 A058406 A058407

Keyword

nonn,tabl

Author

Wolfdieter Lang, Dec 11 2000

Extensions

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

Status

approved