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A335546 Sum of the n-th powers of the (positive) number of permutations of [n] with j descents (j=0..max(0,n-1)).

%I A335546 #18 Sep 03 2021 09:02:23
%S A335546 1,1,2,66,29284,1276095330,1517369276209828,487282023126556473747120,
%T A335546 7083859535826403131254334882236808,
%U A335546 55967865856667137512789954604119317025544887810,29848842646338160810499934016489864718841567718650088748120500
%N A335546 Sum of the n-th powers of the (positive) number of permutations of [n] with j descents (j=0..max(0,n-1)).
%H A335546 Alois P. Heinz, <a href="/A335546/b335546.txt">Table of n, a(n) for n = 0..30</a>
%F A335546 a(n) = A335545(n,n).
%F A335546 a(n) = Sum_{j=0..n} A173018(n,j)^n.
%t A335546 B[n_, k_] := Sum[(-1)^j Binomial[n+1, j] (k-j+1)^n, {j, 0, k+1}];
%t A335546 a[n_] := If[n == 0, 1, Sum[B[n, j]^n, {j, 0, n-1}]];
%t A335546 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Sep 03 2021, from A335545 *)
%Y A335546 Main diagonal of A335545.
%Y A335546 Cf. A008292, A173018, A334623, A335545.
%K A335546 nonn
%O A335546 0,3
%A A335546 _Alois P. Heinz_, Sep 12 2020