A089064 Expansion of e.g.f. log(1-log(1-x)).

0, 1, 0, 1, 1, 8, 26, 194, 1142, 9736, 81384, 823392, 8738016, 104336880, 1328270880, 18419317968, 272291315376, 4312675967232, 72478365279360, 1292173575000192, 24314102888206464, 482046102448383744, 10037081891973037824

Offset

0,6

Comments

Stirling transform of a(n)=[1,0,1,1,8,26,...] is A075792(n)=[1,1,2,8,44,...]. - Michael Somos, Mar 04 2004

Stirling transform of -(-1)^n*a(n)=[1,0,1,-1,8,-26,194,...] is A000142(n-1)=[1,1,2,6,24,120,...]. - Michael Somos, Mar 04 2004

References

G. H. Hardy, A Course of Pure Mathematics, 10th ed., Cambridge University Press, 1960, p. 428.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..451

G. H. Hardy, A Course of Pure Mathematics, Cambridge, The University Press, 1908.

Formula

a(n) = (-1)^(n+1)*Sum_{k=1..n} (k-1)!*Stirling1(n, k).

E.g.f.: log(1-log(1-x)).

a(n) = (n-1)! - Sum_{k=1..n-1} binomial(n-1,k) * (k-1)! * a(n-k). - Seiichi Manyama, Jun 01 2019

Mathematica

nmax = 20; CoefficientList[Series[Log[1-Log[1-x]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 01 2018 *)

Prog

(PARI) a(n)=if(n<0, 0, n!*polcoeff(log(1-log(1-x+x*O(x^n))), n))
(PARI) {a(n) = if (n<1, 0, (n-1)!-sum(k=1, n-1, binomial(n-1, k)*(k-1)!*a(n-k)))} \\ Seiichi Manyama, Jun 01 2019

Crossrefs

Cf. A075792.

Sequence in context: A274733 A223312 A194997 * A240291 A203635 A000810

Adjacent sequences: A089061 A089062 A089063 * A089065 A089066 A089067

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 20 2003

Status

approved