The bicircular-matroid basis conciseness conjecture

Let $b(M)$ denote the number of bases of a matroid $M$, and restrict $b$ to bicircular matroids. A counting function is concise if every positive integer occurs on an input of size polynomial in the logarithm of that integer. Bicircular-matroid basis conjecture. The function $b$ restricted to bicircular matroids is concise. Bicircular matroids give a natural concise presentation for a known $\#\mathrm P$-complete basis-counting problem, but the stronger value-realization bound remains open.