A379611 Table read by rows: T(n, k) = (n + 1)^(n - 1) - (k - 1)*(n + 1)^(n - 2), by convention T(1, 0) = 1.

2, 1, 1, 4, 3, 2, 20, 16, 12, 8, 150, 125, 100, 75, 50, 1512, 1296, 1080, 864, 648, 432, 19208, 16807, 14406, 12005, 9604, 7203, 4802, 294912, 262144, 229376, 196608, 163840, 131072, 98304, 65536, 5314410, 4782969, 4251528, 3720087, 3188646, 2657205, 2125764, 1594323, 1062882

Offset

0,1

Links

Table of n, a(n) for n=0..44.

Steve Butler, Kimberly Hadaway, Victoria Lenius, Preston Martens, and Marshall Moats, Lucky cars and lucky spots in parking functions, arXiv:2412.07873 [math.CO], 2024. See p. 7, corollary 3.1.

Formula

T(n, k) = (n + 1)^(n - 2)*(n - k + 2), if (n, k) != (1, 0).

T(n, k) = (1 - (k - 1)/(n + 1))*(n + 1)^(n - 1), if (n, k) != (1, 0).

Example

Triangle starts:
  [0]      2;
  [1]      1,      1;
  [2]      4,      3,      2;
  [3]     20,     16,     12,      8;
  [4]    150,    125,    100,     75,     50;
  [5]   1512,   1296,   1080,    864,    648,    432;
  [6]  19208,  16807,  14406,  12005,   9604,   7203,  4802;
  [7] 294912, 262144, 229376, 196608, 163840, 131072, 98304, 65536;

Maple

T := (n, k) -> ifelse(n=1 and k=0, 1, (n + 1)^(n - 1) - (k - 1)*(n + 1)^(n - 2)):

Mathematica

T[n_, k_] := T[n, k] = (n + 1)^(n - 1) - (k - 1)*(n + 1)^(n - 2); T[1, 0] := 1;
Flatten@ Table[T[n, k], {n, 0, 8}, {k, 0, n}] (* Michael De Vlieger, Dec 27 2024 *)

Crossrefs

Cf. A007334 (main diagonal), A374756, A375616, A379612 (column 0), A379613.

Sequence in context: A262357 A112744 A249577 * A225924 A078015 A366781

Adjacent sequences: A379608 A379609 A379610 * A379612 A379613 A379614

Keyword

nonn,tabl

Author

Peter Luschny, Dec 27 2024

Status

approved