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

1, 1, 2, 66, 29284, 1276095330, 1517369276209828, 487282023126556473747120, 7083859535826403131254334882236808, 55967865856667137512789954604119317025544887810, 29848842646338160810499934016489864718841567718650088748120500

Offset: 0

Author

Alois P. Heinz, Sep 12 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..30

Crossrefs

Main diagonal of A335545.

Cf. A008292, A173018, A334623, A335545.

Programs

Mathematica

B[n_, k_] := Sum[(-1)^j Binomial[n+1, j] (k-j+1)^n, {j, 0, k+1}];
a[n_] := If[n == 0, 1, Sum[B[n, j]^n, {j, 0, n-1}]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Sep 03 2021, from A335545 *)

Formula

a(n) = A335545(n,n).

a(n) = Sum_{j=0..n} A173018(n,j)^n.