cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A291131 Number of defective parking functions of length n and defect five.

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%I A291131 #11 Feb 24 2019 02:00:42
%S A291131 1,162,12357,710314,36046214,1735513330,82324649310,3930328083098,
%T A291131 191251911975191,9558232936557458,492897541966818651,
%U A291131 26298973648144245066,1454100613639405907108,83377530695619365120818,4959049035365905488761452,305903708967397161238879674
%N A291131 Number of defective parking functions of length n and defect five.
%H A291131 Alois P. Heinz, <a href="/A291131/b291131.txt">Table of n, a(n) for n = 6..386</a>
%H A291131 Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, <a href="https://arxiv.org/abs/0803.0302">Counting Defective Parking Functions</a>, arXiv:0803.0302 [math.CO], 2008.
%F A291131 a(n) ~ (-31*exp(1)/120 + 32*exp(2)/3 - 99*exp(3)/2 + 68*exp(4) - 35*exp(5) + 6*exp(6)) * n^(n-1). - _Vaclav Kotesovec_, Aug 19 2017
%p A291131 S:= (n, k)-> add(binomial(n, i)*k*(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k):
%p A291131 a:= n-> S(n, 5)-S(n, 6):
%p A291131 seq(a(n), n=6..23);
%t A291131 S[n_, k_] := Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}];
%t A291131 a[n_] := S[n, 5] - S[n, 6];
%t A291131 Table[a[n], {n, 6, 23}] (* _Jean-François Alcover_, Feb 24 2019, from Maple *)
%Y A291131 Column k=5 of A264902.
%K A291131 nonn
%O A291131 6,2
%A A291131 _Alois P. Heinz_, Aug 18 2017