A073400 Coefficient triangle of polynomials (falling powers) related to convolutions of A001045(n+1), n >= 0, (generalized (1,2)-Fibonacci). Companion triangle is A073399.

2, 9, 33, 45, 396, 831, 243, 3744, 18297, 28236, 1377, 32481, 273483, 968679, 1210140, 8019, 268029, 3418767, 20681811, 58920534, 62686440, 47385, 2130138, 38186478, 347584284, 1683064737, 4075425738, 3810867480

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) := A001045(n+1), n>= 0, ((1,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073370(n+k,k) = (p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*2*U0(n))/(k!*9^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)= A073399(k,m).

Links

Table of n, a(n) for n=0..27.

Wolfdieter Lang, First 7 rows.

Formula

Recursion for row polynomials defined in the comments: see A073401.

Example

k=2: U2(n)=((9*n+30)*(n+1)*U0(n+1)+(9*n+33)*(n+2)*2*U0(n))/(2*9^2), cf. A073372.
1; 9,33; 45,396,831; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

Crossrefs

Cf. A001045, A073370, A073399, A073401.

Sequence in context: A170872 A123142 A122097 * A048498 A215695 A289600

Adjacent sequences: A073397 A073398 A073399 * A073401 A073402 A073403

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Aug 02 2002

Status

approved