A103910 Triangle T read by rows: inverse of fibonomial triangle (A010048).

1, -1, 1, 0, -1, 1, 1, 0, -2, 1, -1, 3, 0, -3, 1, -6, -5, 15, 0, -5, 1, 35, -48, -40, 60, 0, -8, 1, 181, 455, -624, -260, 260, 0, -13, 1, -6056, 3801, 9555, -6552, -1820, 1092, 0, -21, 1, -3741, -205904, 129234, 162435, -74256, -12376, 4641, 0, -34, 1

Offset

1,9

Comments

Conjecture: all rows except the first add to zero.

Links

Table of n, a(n) for n=1..55.

M. Dziemianczuk, On multi F-nomial coefficients and Inversion formula for F-nomial coefficients, Preprint: arXiv:0806.3626, 23 Jun 2008

Formula

Conjecture: T(n+k, n) = A010048(n+k-1, k)*T(k, 1), n>1.

a(n,k) = A010048(n,k) * (Sum[s=1..n-k;(-1)^s * Sum[k1+k2+..+ks=n-k,ki>=1; C(n-k; k1,k2,...,ks)] ]) where C(n; k1,k2,...,ks) is a multi-F-nomial coefficient. - Maciej Dziemianczuk, Dec 21 2008

Example

1,
-1,1,
0,-1,1,
1,0,-2,1,
-1,3,0,-3,1,
-6,-5,15,0,-5,1,
35,-48,-40,60,0,-8,1,
181,455,-624,-260,260,0,-13,1,
-6056,3801,9555,-6552,-1820,1092,0,-21,1,

Crossrefs

First column is in A103995.

Sequence in context: A245840 A033774 A033804 * A155993 A353630 A341091

Adjacent sequences: A103907 A103908 A103909 * A103911 A103912 A103913

Keyword

sign,tabl

Author

Ralf Stephan, Feb 24 2005

Status

approved