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

1, 9, 30, 63, 531, 1050, 405, 6165, 29610, 44520, 2511, 59454, 502821, 1789614, 2245320, 15309, 517104, 6686631, 41182344, 120133692, 131891760, 92583, 4214349, 76790673, 714174327, 3559509360, 8966770308, 8862693840

Offset

0,2

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) := 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 q(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A073400(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; 9,30; 63,531,1050; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

Crossrefs

Cf. A001045, A073370, A073400-A073402, A073372.

Sequence in context: A063161 A295867 A195319 * A225275 A005919 A084370

Adjacent sequences: A073396 A073397 A073398 * A073400 A073401 A073402

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Aug 02 2002

Status

approved