This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A058405 #8 Aug 29 2019 09:12:22 %S A058405 2,8,20,48,288,360,320,3520,11360,9840,2176,37888,225344,522752, %T A058405 363360,14848,373504,3491072,14871296,27849600,16776000,101376, %U A058405 3467264,46459904,308703232,1053556480,1692808704,922158720,692224,30834688 %N A058405 Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058404. %C A058405 The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,.. %C A058405 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). %H A058405 W. Lang, <a href="/A058404/a058404_5.txt">First 7 rows, also for A058404</a>. %F A058405 Recursion for row polynomials defined in the comments: see A058402. %e A058405 k=2: P2(n)=((8*n+22)*(n+1)*2*P0(n+1)+(8*n+20)*(n+2)*P0(n))/128, cf. A054457. %e A058405 2; 8,20; 48,288,360; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0) %Y A058405 Cf. A000129, A054456, A058404, A054457, A058402-3 (rising powers). %K A058405 nonn,tabl %O A058405 0,1 %A A058405 _Wolfdieter Lang_, Dec 11 2000 %E A058405 Link and cross-references added by _Wolfdieter Lang_, Jul 31 2002