A099731 This table shows the coefficients of sum formulas of n-th Fibonacci numbers (A000045). The k-th row (k>=1) contains T(i,k) for i=1 to k, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies F(n)= Sum_{i=1..k} T(i,k) * n^(k-i)/(k-1)!.

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

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 k-th row we obtain k=7 and the coefficients
T(i,7) will be the following: 1,-51,1135,-13665,93544,-342324,523440,
=> F(13) = [13^6-51*13^5+1135*13^4-13665*13^3+93544*13^2-342324*13+523440]/6! = 233.

Crossrefs

Cf. A000045, A094638.

Sequence in context: A370131 A258150 A330599 * A307716 A091306 A374538

Adjacent sequences: A099728 A099729 A099730 * A099732 A099733 A099734

Keyword

sign,tabl

Author

André F. Labossière, Nov 08 2004

Status

approved