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 *)
Table[(-1)^(n+1) * Sum[(k-1)! * StirlingS1[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 19 2024 *)
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Dec 20 2003
STATUS
approved