A347492 Irregular triangle read by rows: T(n, k) is the q-multinomial coefficient defined by the k-th partition of n in Abramowitz-Stegun order, evaluated at q = 11.
1, 1, 12, 1, 133, 1596, 1, 1464, 16226, 194712, 2336544, 1, 16105, 1964810, 23577720, 261319730, 3135836760, 37630041120, 1, 177156, 237758115, 2617126920, 2853097380, 348077880360, 3857863173990, 4176934564320, 46294358087880, 555532297054560, 6666387564654720, 1, 1948717
Offset: 1
Examples
The number of subspace chains 0 < V_1 < V_2 < (F_11)^3 is 1596 = T(3, (1, 1, 1)). There are 133 = A022175(3, 1) choices for a one-dimensional subspace V_1 and, for each of them, 12 = A022175(2, 1) extensions to a two-dimensional subspace V_2.
Triangle begins:
k: 1 2 3 4 5
---------------------------
n=1: 1
n=2: 1 12
n=3: 1 133 1596
n=4: 1 1464 16226 194712 2336544
References
- R. P. Stanley, Enumerative Combinatorics (vol. 1), Cambridge University Press (1997), Section 1.3.
Links
- Álvar Ibeas, First 20 rows, flattened
Formula
T(n, (n)) = 1. T(n, L) = A022175(n, e) * T(n - e, L \ {e}), if L is a partition of n and e < n is a part of L.
Comments