OFFSET
0,2
COMMENTS
The row polynomials are p(k,x) := sum(a(k,m)*x^m,m=0..k), k=0,1,2,...
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^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A073406(k,m).
LINKS
W. Lang, First 7 rows.
FORMULA
Recursion for row polynomials defined in the comments: p(k, n)= 2*(2*(n+2)*p(k-1, n+1)+2*(n+2*(k+1))*p(k-1, n)+(n+3)*q(k-1, n)); q(k, n)= 4*((n+1)*p(k-1, n+1)+(n+2*(k+1))*q(k-1, n)), k >= 1.
EXAMPLE
k=2: U2(n)=2*((36+12*n)*(n+1)*U0(n+1)+(36+12*n)*(n+2)*U0(n))/(2!*12^2), cf. A073389.
Triangle begins:
1;
36, 12;
1536, 888, 120;
... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved