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A073399 Coefficient triangle of polynomials (falling powers) related to convolutions of A001045(n+1), n>=0, (generalized (1,2)-Fibonacci). Companion triangle is A073400. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A063161 A295867 A195319 * A225275 A005919 A084370
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved

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Last modified February 23 10:03 EST 2024. Contains 370276 sequences. (Running on oeis4.)