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A058403 Coefficient triangle of polynomials (rising powers) related to Pell number convolutions. Companion triangle is A058402. 3
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 (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^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: A077341 A076495 A308387 * A083297 A221921 A012739

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

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Last modified February 18 09:15 EST 2020. Contains 332011 sequences. (Running on oeis4.)