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

2, 12, 36, 96, 672, 1056, 864, 10752, 40416, 43968, 8064, 156672, 1051776, 2815488, 2396160, 76032, 2121984, 22125312, 105981696, 226492416, 161879040, 718848, 27205632, 404656128, 2995605504

Offset

0,1

Comments

The row polynomials are q(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!*(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).

Links

Table of n, a(n) for n=0..24.

W. Lang, First 7 rows.

Formula

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

Example

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; 96,672,1056; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

Crossrefs

Cf. A002605, A073387, A073403, A073405.

Sequence in context: A011379 A338610 A369175 * A141208 A181825 A169630

Adjacent sequences: A073401 A073402 A073403 * A073405 A073406 A073407

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Aug 02 2002

Status

approved