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.
%I A298593 #42 Mar 05 2018 04:19:43 %S A298593 1,4,2,24,15,9,200,136,100,64,2160,1535,1215,945,625,28812,21036, %T A298593 17286,14406,11526,7776,458752,341103,286671,247296,211456,172081, %U A298593 117649,8503056,6405904,5464712,4811528,4251528,3691528,3038344,2097152,180000000,136953279,118078911,105372819,94921875,85078125,74627181,61921089,43046721 %N A298593 Triangle read by rows: T(n,k) = number of times the value k appears on the parking functions of length n. %C A298593 T(n,k) is the number of pairs (f,i) such that f is a parking function and f(i) = k. %F A298593 T(n,k) = n*Sum_{j=k..n} binomial(n-1, j-1)*j^(j-2)*(n+1-j)^(n-1-j). %F A298593 T(n,k) = n*A298592(n,k). %F A298593 T(n,k) = n*Sum_{j=k..n} A298594(n,j). %F A298593 T(n,k) = Sum_{j=k..n} A298597(n,j). %F A298593 Sum_{k=1..n} T(n,k) = n*A000272(n+1). %F A298593 T(n+1,1) = A089946(n), T(n,n) = A000169(n). - _Andrey Zabolotskiy_, Feb 21 2018 %e A298593 Triangle begins: %e A298593 ==================================================================== %e A298593 n\k| 1 2 3 4 5 6 7 8 %e A298593 ---|---------------------------------------------------------------- %e A298593 1 | 1 %e A298593 2 | 4 2 %e A298593 3 | 24 15 9 %e A298593 4 | 200 136 100 64 %e A298593 5 | 2160 1535 1215 945 625 %e A298593 6 | 28812 21036 17286 14406 11526 7776 %e A298593 7 | 458752 341103 286671 247296 211456 172081 117649 %e A298593 8 | 8503056 6405904 5464712 4811528 4251528 3691528 3038344 2097152 %e A298593 ... %t A298593 Table[n Sum[Binomial[n - 1, j - 1] j^(j - 2)*(n + 1 - j)^(n - 1 - j), {j, k, n}], {n, 9}, {k, n}] // Flatten (* _Michael De Vlieger_, Jan 22 2018 *) %Y A298593 Cf. A000169, A000272, A089946, A298592, A298594, A298597. %K A298593 easy,nonn,tabl %O A298593 1,2 %A A298593 _Rui Duarte_, Jan 22 2018