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A058404 Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058405. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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: A124701 A002968 A211530 * A211479 A318034 A326162

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

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)