A246040 a(1)=1; a(n)=Sum_{k=1..n-1} Stirling_1(n,k)*a(k).

1, -1, 5, -47, 719, -16299, 513253, -21430513, 1145710573, -76317960163, 6197399680779, -602640663660199, 69134669061681469, -9239224408001877873, 1422887941494773642817, -250160794466824215921275, 49797413478450579190546203, -11142367835115998962269070519, 2784355004138005473128335461749

Offset: 1

Author

N. J. A. Sloane, Aug 22 2014

Keywords

• sign

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

• D. Barsky, J.-P. Bézivin, p-adic Properties of Lengyel's Numbers, Journal of Integer Sequences, 17 (2014), #14.7.3. See Y_n.

Crossrefs

A signed version of A086555.

Cf. A005121, A260932.

Programs

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 *)

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