A052342 - OEIS

%I #12 Sep 01 2022 04:59:11

%S 1,1,0,-2,6,250,-27090,-20110502,100802987166,4068016202512330,

%T -1476018746725429261650,-5356258014516256268708458502,

%U 213804326403655009107321872257070526,102412631111025007566217285932140576241712810

%N Shifts left under Stirling-Bernoulli transform.

%H Alois P. Heinz, <a href="/A052342/b052342.txt">Table of n, a(n) for n = 0..40</a>

%F Stirling-Bernoulli transform sends a to b where b(n) = Sum_{i=0..n} (-1)^i*i!*S(n+1, i+1)*b(i).

%p a:= proc(n) option remember; `if`(n<1, 1,

%p       add((-1)^k*k!*Stirling2(n, k+1)*a(k), k=0..n-1))

%p     end:

%p seq(a(n), n=0..15);  # _Alois P. Heinz_, May 17 2013

%t a[n_] := a[n] = If[n<1, 1, Sum[(-1)^k*k!*StirlingS2[n, k+1]*a[k], {k, 0, n-1}]];

%t Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Sep 01 2022, after _Alois P. Heinz_ *)

%K sign,eigen

%O 0,4

%A _Christian G. Bower_, Jan 09 2000