A328694 a(n) = sum of lead terms of all parking functions of length n.

1, 4, 27, 257, 3156, 47442, 843352, 17300943, 402210240, 10448526896, 299925224064, 9426724628301, 321959469056512, 11872685912032350, 470132249600142336, 19895288956008203963, 896055382220853362688, 42793946679993786078108, 2160123874888094765056000

Offset: 1

Author

Andrew Howroyd, Oct 25 2019

Keywords

• nonn

Examples

			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.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024. See pp. 18, 22.

Crossrefs

Cf. A298592, A318047.

Programs

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))}

Formula

a(n) = Sum_{k=1..n} k*A298592(n,k).

a(n) = A318047(n) / n.