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A324360 Total number of occurrences of 10 in the (signed) displacement sets of all permutations of [n+10] divided by 10!.

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%I A324360 #9 Sep 04 2023 11:01:18
%S A324360 0,1,21,364,6115,104226,1834205,33576236,641293047,12792063934,
%T A324360 266464077769,5792423481120,131276423686979,3098383343174978,
%U A324360 76066855087291221,1940223116685166996,51356370210296015215,1409053932006095867526,40028877611196977481857
%N A324360 Total number of occurrences of 10 in the (signed) displacement sets of all permutations of [n+10] divided by 10!.
%H A324360 Alois P. Heinz, <a href="/A324360/b324360.txt">Table of n, a(n) for n = 0..442</a>
%H A324360 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A324360 E.g.f.: (1-exp(-x))/(1-x)^11.
%F A324360 a(n) = -1/10! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+10-j)!.
%F A324360 a(n) = A306234(n+10,10).
%p A324360 a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(10):
%p A324360 seq(a(n), n=0..23);
%t A324360 With[{nn=20},CoefficientList[Series[(1-Exp[-x])/(1-x)^11,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 04 2023 *)
%Y A324360 Column k=10 of A324362.
%Y A324360 Cf. A306234.
%K A324360 nonn
%O A324360 0,3
%A A324360 _Alois P. Heinz_, Feb 23 2019