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A073404 Coefficient triangle of polynomials (falling powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073403.

%I A073404 #12 Aug 29 2019 13:19:38
%S A073404 2,12,36,96,672,1056,864,10752,40416,43968,8064,156672,1051776,
%T A073404 2815488,2396160,76032,2121984,22125312,105981696,226492416,161879040,
%U A073404 718848,27205632,404656128,2995605504
%N A073404 Coefficient triangle of polynomials (falling powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073403.
%C A073404 The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..
%C A073404 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!*(2^2+4*2)^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)= A073403(k,m).
%H A073404 W. Lang, <a href="/A073403/a073403_4.txt">First 7 rows</a>.
%F A073404 Recursion for row polynomials defined in the comments: see A073405.
%e A073404 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 A073404 1; 12,36; 96,672,1056; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
%Y A073404 Cf. A002605, A073387, A073403, A073405.
%K A073404 nonn,easy,tabl
%O A073404 0,1
%A A073404 _Wolfdieter Lang_, Aug 02 2002