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

1, 12, 36, 120, 888, 1536, 1152, 15168, 62592, 80448, 10944, 222336, 1600704, 4813056, 5068800, 103680, 2992896, 32811264, 169917696, 413351424, 375598080, 981504, 38112768, 587976192, 4592982528

Offset: 0

Author

Wolfdieter Lang, Aug 02 2002

Keywords

• nonn
• easy
• tabl

Comments

The row polynomials are p(k,x) := sum(a(k,m)*x^(k-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^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A073404(k,m).

Examples

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

Links

• W. Lang, First 7 rows.

Crossrefs

Cf. A002605, A073387, A073404.

Formula

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