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

Author

Wolfdieter Lang, Dec 11 2000

Keywords

• nonn
• tabl

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).

Examples

			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)
		

Links

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

Crossrefs

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

Formula

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

Extensions

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