A073403 - OEIS

%I #12 Aug 29 2019 13:19:09

%S 1,12,36,120,888,1536,1152,15168,62592,80448,10944,222336,1600704,

%T 4813056,5068800,103680,2992896,32811264,169917696,413351424,

%U 375598080,981504,38112768,587976192,4592982528

%N Coefficient triangle of polynomials (falling powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073404.

%C The row polynomials are p(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..

%C The k-th convolution of U0(n) := A002605(n), n>= 0, ((2,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073387(n+k,k) = 2*(p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*U0(n))/(k!*12^k), k=1,2,..., where the companion polynomials q(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A073404(k,m).

%H W. Lang, <a href="/A073403/a073403_4.txt">First 7 rows</a>.

%F Recursion for row polynomials defined in the comments: see A073405.

%e k=2: U2(n)=(2*(36+12*n)*(n+1)*U0(n+1)+2*(36+12*n)*(n+2)*U0(n))/(2!*12^2), cf. A073389.

%e 1; 12,36; 120,888,1536; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

%Y Cf. A002605, A073387, A073404.

%K nonn,easy,tabl

%O 0,2

%A _Wolfdieter Lang_, Aug 02 2002