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A073406 Coefficient triangle of polynomials (rising powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073405. 3

%I

%S 2,36,12,1056,672,96,43968,40416,10752,864,2396160,2815488,1051776,

%T 156672,8064,161879040,226492416,105981696,22125312,2121984,76032,

%U 13044326400,20766633984,11446769664,2995605504

%N Coefficient triangle of polynomials (rising powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073405.

%C The row polynomials are q(k,x) := sum(a(k,m)*x^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 p(k,n) := sum(b(k,m)*n^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A073405(k,m).

%H W. Lang, <a href="http://www.itp.kit.edu/~wl/EISpub/A073405_6.text">First 7 rows</a>.

%F Recursion for row polynomials defined in the comments: p(k, n)= 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.

%e 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.

%e 2; 36,12; 1056,672,96; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

%Y Cf. A002605, A073387, A073403-A073405.

%K nonn,easy,tabl

%O 0,1

%A _Wolfdieter Lang_, Aug 02 2002

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Last modified July 23 19:33 EDT 2019. Contains 325263 sequences. (Running on oeis4.)