[seqfan] Fibonomial multichoose

[Dale Gerdemann]

Hi Seqfans,

The following table shows the fibonomial version of multichoose:

1, 1, 1, 1, 1, 1, 1, 1, 1, ...

0, 1, 1, 2, 3, 5, 8, 13, 21, ...

0, 1, 2, 6, 15, 40, 104, 273, 714, ...

0, 1, 3, 15, 60, 260, 1092, 4641, 19635, ...

0, 1, 5, 40, 260, 1820, 12376, 85085, 582505, ...

0, 1, 8, 104, 1092, 12376, 136136, 1514513, 16776144, ...

0, 1, 13, 273, 4641, 85085, 1514513, 27261234, 488605194, ...

0, 1, 21, 714, 19635, 582505, 16776144, 488605194, 14169550626, ...

0, 1, 34, 1870, 83215, 3994320, 186135312, 8771626578, 411591708660, ...

0, 1, 55, 4895, 352440, 27372840, 2063912136, 157373300370,
11948265189630,...

...

The rows are A000012, A000045, A001654, A001655, A001656, A001657, A001658,
A056565, A056566, A056567, ...


The array is completely analogous to the array in A071919. So just as
multichoose(n,k) = binomial(n+k-1,k), fibonomialMultichoose(n,k) =
fibonomial(n+k-1,k). And just as multichoose(n,k) =
risingFactorial(n,k)/k!, fibonomialMultichoose(n,k) =
risingFibonorial(n,k)/fibonorial(k).

So wouldn't this be a reasonable addition to the OEIS?


Dale