A087761 Expansion of (1-x)^(1/(x-1)).

1, 1, 4, 21, 140, 1130, 10674, 115206, 1396016, 18739080, 275712840, 4408612560, 76070179272, 1408041937848, 27816773482848, 583970117197320, 12978149959718400, 304310928180279360, 7506092106055537344

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..439

Formula

a(n) = Sum_{k=0..n} |Stirling1(n, k)|*A000248(k).

From Paul D. Hanna, Mar 17 2010: (Start)

E.g.f.: exp( Sum_{n>=1} H(n)*x^n ) where H(n) is the n-th harmonic number;

a(n) = (n-1)!*Sum_{k=0..n-1} (n-k)*H(n-k)*a(k)/k! for n>0 with a(0)=1. (End)

Empirical: a(n) = Sum_{i=0..n} binomial(n,i)*A005727(i)*(n-1)!/(i-1)! for n>0. - John M. Campbell, Dec 13 2016

Mathematica

Table[Sum[BellY[n, k, Table[m! HarmonicNumber[m], {m, n}]], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Prog

(PARI) a(n)=if(n==0, 1, (n-1)!*sum(k=0, n-1, (n-k)*sum(j=1, n-k, 1/j)*a(k)/k!)) \\ Paul D. Hanna, Mar 17 2010; corrected Mar 19 2010

Crossrefs

Cf. A000248, A005727.

Sequence in context: A349534 A222058 A265174 * A245503 A120368 A053482

Adjacent sequences: A087758 A087759 A087760 * A087762 A087763 A087764

Keyword

nonn

Author

Vladeta Jovovic, Oct 02 2003

Status

approved