cp's OEIS Frontend

A062134 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).

%I A062134 #8 Apr 20 2025 03:24:17
%S A062134 1,2,0,8,24,16,336,832,576,128,12480,28480,23680,8960,1280,481920,
%T A062134 1208832,1167360,552960,130560,12288,22786560,61834752,65709056,
%U A062134 35911680,10895360,1763328,118784,1280885760,3645444096
%N A062134 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).
%C A062134 The row polynomials pPL1(n,x) := Sum_{m=0..n} A062133(n,m)*x^m and pPL2(n,x) := Sum_{m=0..n} a(n,m)*x^m appear in the k-fold convolution of the associated Pell numbers PL(n) := A001333(n+1), n >= 0, as follows: PL(k; n) := A054458(n+k,k) = (2*pPL1(k,n)*PL(n+1)+pPL2(k,n)*PL(n))/(k!*8^k), k >= 0.
%e A062134 Triangle begins:
%e A062134   {1};
%e A062134   {2,0};
%e A062134   {8,24,16};
%e A062134   {336,832,576,128};
%e A062134   ...
%e A062134 pPL1(1,n) = 1+2*n.
%e A062134 pPL2(1,n) = 2.
%e A062134 PL(1; n) = A054459(n) = ((1+2*n)*PL(n+1)+PL(n))/4.
%Y A062134 Cf. A062133(n, m) (companion triangle), A054458(n, m) (convolution triangle).
%K A062134 nonn,tabl,more
%O A062134 0,2
%A A062134 _Wolfdieter Lang_, Jun 19 2001