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A328694 a(n) = sum of lead terms of all parking functions of length n. 1

%I

%S 1,4,27,257,3156,47442,843352,17300943,402210240,10448526896,

%T 299925224064,9426724628301,321959469056512,11872685912032350,

%U 470132249600142336,19895288956008203963,896055382220853362688,42793946679993786078108,2160123874888094765056000

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

%H Andrew Howroyd, <a href="/A328694/b328694.txt">Table of n, a(n) for n = 1..200</a>

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

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

%e 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.

%o (PARI) \\ here T(n,k) is A298592(n,k).

%o T(n, k)={sum(j=k, n, binomial(n-1, j-1)*j^(j-2)*(n+1-j)^(n-1-j))}

%o a(n)={sum(k=1, n, k*T(n, k))}

%Y Cf. A298592, A318047.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Oct 25 2019

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Last modified June 13 13:38 EDT 2021. Contains 344999 sequences. (Running on oeis4.)