cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A329058 2-parking triangle T(r, i, 2) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 2 and 0 <= i <= r.

This page as a plain text file.
%I A329058 #10 Nov 05 2019 09:49:56
%S A329058 1,2,1,7,6,3,30,36,32,16,143,220,275,250,125,728,1365,2184,2808,2592,
%T A329058 1296,3876,8568,16660,27440,36015,33614,16807,21318,54264,124032,
%U A329058 248064,417792,557056,524288,262144,120175,346104,908523,2133054,4363065,7479540,10097379,9565938,4782969
%N A329058 2-parking triangle T(r, i, 2) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 2 and 0 <= i <= r.
%C A329058 The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).
%H A329058 Stefano Spezia, <a href="/A329058/b329058.txt">First 151 rows of the triangle, flattened</a>
%H A329058 Martha Yip, <a href="https://arxiv.org/abs/1910.10060">A Fuss-Catalan variation of the caracol flow polytope</a>, arXiv:1910.10060 [math.CO], 2019.
%F A329058 T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).
%F A329058 T(r, 0, 2) = A006013(r).
%F A329058 T(r, r, 2) = A000272(r + 1).
%e A329058 r/i|   0   1   2   3   4
%e A329058 ————————————————————————
%e A329058 0  |   1
%e A329058 1  |   2   1
%e A329058 2  |   7   6   3
%e A329058 3  |  30  36  32  16
%e A329058 4  | 143 220 275 250 125
%t A329058 T[r_, i_,k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r,i,2],{r,0,9},{i,0,r}]]
%Y A329058 Cf. A000108, A000272, A006013, A007318, A329057, A329059, A329060, A329113 (row sums).
%K A329058 nonn,tabl
%O A329058 0,2
%A A329058 _Stefano Spezia_, Nov 02 2019