OFFSET
0,3
COMMENTS
Note that odd values for n>=65 are negative. - Vaclav Kotesovec, Jun 28 2013
FORMULA
a(n)=sum(m=1..n, binomial(n,m)*sum(k=1..n-m, k!*(sum(i=0..k, binomial(m,k-i)*binomial(m+i-1,m-1)))*stirling1(n-m,k)))+1.
MATHEMATICA
Table[Sum[Binomial[n, m]*Sum[k!*Sum[Binomial[m, k-i]*Binomial[m+i-1, m-1], {i, 0, k}]*StirlingS1[n-m, k], {k, 1, n-m}], {m, 1, n}]+1, {n, 0, 20}] (* Vaclav Kotesovec, Jun 27 2013 *)
With[{nn=20}, CoefficientList[Series[Exp[x (1+Log[1+x])/(1-Log[1+x])], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 03 2015 *)
PROG
(Maxima)
a(n):=sum(binomial(n, m)*sum(k!*(sum(binomial(m, k-i)*binomial(m+i-1, m-1), i, 0, k))*stirling1(n-m, k), k, 1, n-m), m, 1, n)+1;
(PARI) a(n)=sum(m=1, n, binomial(n, m)*sum(k=1, n-m, k!*sum(i=0, k, binomial(m, k-i)*binomial(m+i-1, m-1)))*stirling(n-m, k))+1 \\ Charles R Greathouse IV, Jun 28 2013
(PARI) x = 'x + O('x^66);
egf = exp(x*(1+log(1+x))/(1-log(1+x)));
Vec(serlaplace(egf)) \\ Joerg Arndt, Jun 29 2013
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Nov 06 2011
STATUS
approved