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A058405 Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058404. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
Wolfdieter Lang, Dec 11 2000
EXTENSIONS
Link and cross-references added by Wolfdieter Lang, Jul 31 2002
STATUS
approved

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Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)