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

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

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

Cf. A298592, A318047.

Sequence in context: A360728 A353014 A360731 * A353015 A360032 A360833

Adjacent sequences: A328691 A328692 A328693 * A328695 A328696 A328697

Keyword

nonn

Author

Andrew Howroyd, Oct 25 2019

Status

approved