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A328694
a(n) = sum of lead terms of all parking functions of length n.
2
1, 4, 27, 257, 3156, 47442, 843352, 17300943, 402210240, 10448526896, 299925224064, 9426724628301, 321959469056512, 11872685912032350, 470132249600142336, 19895288956008203963, 896055382220853362688, 42793946679993786078108, 2160123874888094765056000
OFFSET
1,2
LINKS
Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024. See pp. 18, 22.
FORMULA
a(n) = Sum_{k=1..n} k*A298592(n,k).
a(n) = A318047(n) / n.
EXAMPLE
Case n = 2: There are 3 parking functions of length 2: [1, 1], [1, 2], [2, 1]. Summing up the initial values gives 1 + 1 + 2 = 4, so a(2) = 4.
PROG
(PARI) \\ here T(n, k) is A298592(n, k).
T(n, k)={sum(j=k, n, binomial(n-1, j-1)*j^(j-2)*(n+1-j)^(n-1-j))}
a(n)={sum(k=1, n, k*T(n, k))}
CROSSREFS
Sequence in context: A360728 A353014 A360731 * A353015 A360032 A360833
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 25 2019
STATUS
approved