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 A058404 #8 Aug 29 2019 13:14:20 %S A058404 1,8,22,56,376,588,384,4576,17024,19656,2624,48256,313504,848096, %T A058404 801360,17920,468608,4643072,21685888,47494272,38797920,122368, %U A058404 4307456,60136448,424509952,1590913920,2986217856,2181332160,835584,38055936 %N A058404 Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058405. %C A058404 The row polynomials are p(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,.. %C A058404 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). %C A058404 a(k,0)= A057084(k), k >= 0 (conjecture). %H A058404 W. Lang, <a href="/A058404/a058404_5.txt">First 7 rows, also for A058405</a>. %F A058404 Recursion for row polynomials defined in the comments: see A058402. %e A058404 k=2: P2(n)=(8*n+22)*(n+1)*2*P0(n+1)+(8*n+20)*(n+2)*P0(n))/128, cf. A054457. %e A058404 1; 8,22; 56,376,588; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0) %Y A058404 Cf. A000129, A054456, A058405, A054457, A057084, A058402-3 (rising powers). %K A058404 nonn,tabl %O A058404 0,2 %A A058404 _Wolfdieter Lang_, Dec 11 2000 %E A058404 Link and cross-references added by _Wolfdieter Lang_, Jul 31 2002