A057282 -id:A057282 - cp's OEIS frontend

A057281 Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057282.

1, 5, 16, 20, 160, 300, 75, 1075, 4850, 6840, 275, 6100, 48175, 159650, 186120, 1000, 31550, 379700, 2168650, 5846700, 5916240, 3625, 153875, 2605175, 22426825, 103057800, 238437900, 215717040, 13125, 720375, 16273875, 195469125

Offset: 0

Wolfdieter Lang, Sep 13 2000

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 F0(n) := A000045(n+1), n >= 0, (Fibonacci numbers starting with F0(0)=1) with itself is Fk(n) := A037027(n+k,k) = (p(k-1,n)*(n+1)*F0(n+1) + q(k-1,n)*(n+2)*F0(n))/(k!*5^k), k=1,2,..., where the companion polynomials q(k,n) := sum(b(k,m)*n^(k-m),m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057282(k,m).
a(k,0)= A030191(k), k >= 0.

			k=2: F2(n)=((5*n^2+21*n+16)*F(n+2)+(5*n^2+27*n+34)*F(n+1))/50, F(n)=A000045(n); see A001628.

Cf. A000045, A037027, A057995, A057280, A057282.

A151615 Row sums of A057282.

Original entry on oeis.org

2, 22, 360, 7880, 216240, 7124880, 273463680

Offset: 1

N. J. A. Sloane, May 29 2009

nonn

# read in A057282 as list called s1
f:=n->add(s1[i],i=n*(n-1)/2+1..n*(n+1)/2); [seq(f(n),n=1..7)];

cp's OEIS Frontend

A057281 Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057282.

Views

Author

Keywords

Comments

Examples

Crossrefs

A151615 Row sums of A057282.

Views

Author

Keywords

Programs

Maple