|
|
A246040
|
|
a(1)=1; a(n)=Sum_{k=1..n-1} Stirling_1(n,k)*a(k).
|
|
4
|
|
|
1, -1, 5, -47, 719, -16299, 513253, -21430513, 1145710573, -76317960163, 6197399680779, -602640663660199, 69134669061681469, -9239224408001877873, 1422887941494773642817, -250160794466824215921275, 49797413478450579190546203, -11142367835115998962269070519, 2784355004138005473128335461749
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
2*Sum_{k>=1} a(k-1)/fallfac(n,k) = -1/n + Sum_{k>=1} (1 + a(k-1))/n^k, with the falling factorials fallfac(n,k) = Product_{j=0..k-1}(n-j). - Vaclav Kotesovec, Aug 04 2015
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ (-1)^(n+1) * c * n!^2 / (n^(1-log(2)/3) * (2*log(2))^n), where c = A260932 = 0.9031646749584662473216609915945142350500875792441051556... . - Vaclav Kotesovec, Aug 04 2015
|
|
MAPLE
|
with(combinat);
Y:=proc(n) option remember; local k; if n=1 then 1 else add(stirling1(n, k)*Y(k), k=1..n-1); fi; end;
[seq(Y(n), n=1..35)];
|
|
MATHEMATICA
|
Clear[a]; a[1] = 1; a[n_] := a[n] = Sum[StirlingS1[n, k]*a[k], {k, 1, n-1}]; Table[a[n], {n, 1, 20}] (* Vaclav Kotesovec, Aug 04 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|