

A099731


This table shows the coefficients of sum formulas of nth Fibonacci numbers (A000045). The kth row (k>=1) contains T(i,k) for i=1 to k, where k=[2*n+1+(1)^(n1)]/4 and T(i,k) satisfies F(n)= Sum_{i=1..k} T(i,k) * n^(ki)/(k1)!.


15



1, 1, 1, 1, 5, 10, 1, 12, 59, 90, 1, 22, 203, 830, 1320, 1, 35, 525, 3985, 15374, 23640, 1, 51, 1135, 13665, 93544, 342324, 523440, 1, 70, 2170, 37870, 399889, 2542540, 8997540, 13633200, 1, 92, 3794, 90440, 1356929, 13076588, 78896236, 271996080, 409852800, 1, 117, 6198, 193410
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OFFSET

1,5


LINKS

Table of n, a(n) for n=1..49.


EXAMPLE

F(13)=233; substituting n=13 in the formula of the kth row we obtain k=7 and the coefficients
T(i,7) will be the following: 1,51,1135,13665,93544,342324,523440,
=> F(13) = [13^651*13^5+1135*13^413665*13^3+93544*13^2342324*13+523440]/6! = 233.


CROSSREFS

Cf. A000045, A094638.
Sequence in context: A357280 A258150 A330599 * A307716 A091306 A073048
Adjacent sequences: A099728 A099729 A099730 * A099732 A099733 A099734


KEYWORD

sign,tabl


AUTHOR

André F. Labossière, Nov 08 2004


STATUS

approved



