A058405 -id:A058405 - cp's OEIS frontend

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

Wolfdieter Lang, Dec 11 2000

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).

			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)

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

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

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

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

cp's OEIS Frontend

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

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