reviewed

approved

proposed

reviewed

editing

proposed

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 [From . - _Maciej Dziemianczuk (maciek.ciupa(AT)gmail.com), _, Dec 21 2008]

_Ralf Stephan, _, Feb 24 2005

approved

editing

M. Dziemianczuk, <a href="http://arxiv.org/abs/0806.3626">On multi F-nomial coefficients and Inversion formula for F-nomial coefficients</a>, Preprint: arXiv:0806.3626, 23 Jun 2008

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 [From Maciej Dziemianczuk (maciek.ciupa(AT)gmail.com), Dec 21 2008]

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

sign,tabl,new

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

1,9

Conjecture: all rows except the first add to zero.

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

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,

First column is in A103995.

sign,tabl

Ralf Stephan, Feb 24 2005

approved