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 A073402 #25 Nov 25 2024 20:44:27 %S A073402 2,33,9,831,396,45,28236,18297,3744,243,1210140,968679,273483,32481, %T A073402 1377,62686440,58920534,20681811,3418767,268029,8019,3810867480, %U A073402 4075425738,1683064737,347584284,38186478,2130138,47385 %N A073402 Coefficient triangle of polynomials (rising powers) related to convolutions of A001045(n+1), n >= 0, (generalized (1,2)-Fibonacci). Companion triangle is A073401. %C A073402 The row polynomials are q(k,x) := sum(a(k,m)*x^m,m=0..k), k=0,1,2,... %C A073402 The k-th convolution of U0(n) := A001045(n+1), n>= 0, ((1,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073370(n+k,k) = (p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*2*U0(n))/(k!*9^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)= A073401(k,m). %H A073402 Sean A. Irvine, <a href="/A073402/b073402.txt">Table of n, a(n) for n = 0..989</a> %H A073402 Wolfdieter Lang, <a href="/A073401/a073401.txt">First 7 rows</a>. %F A073402 Recursion for row polynomials defined in the comments: p(k, n)= (n+2)*p(k-1, n+1)+4*(n+2*(k+1))*p(k-1, n)+2*(n+3)*q(k-1, n+1); q(k, n)= (n+1)*p(k-1, n+1)+4*(n+2*(k+1))*q(k-1, n), k >= 1. [Corrected by _Sean A. Irvine_, Nov 25 2024] %e A073402 k=2: U2(n)=((30+9*n)*(n+1)*U0(n+1)+(33+9*n)*(n+2)*2*U0(n))/(2*9^2), cf. A073372. %e A073402 1; 33,9; 831,396,45; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0). %Y A073402 Cf. A001045, A073370, A073399, A073372, A073400. %K A073402 nonn,easy,tabl %O A073402 0,1 %A A073402 _Wolfdieter Lang_, Aug 02 2002