A199480 E.g.f. exp(x*(1+log(1+x))/(1-log(1+x)))

1, 1, 5, 19, 113, 701, 5269, 42883, 393441, 3887065, 42013381, 484389731, 6008730001, 78857557013, 1101462510485, 16168488228691, 250664264773825, 4061840593263921, 69116855497839109, 1223722811124319219, 22651504652950552241

Offset

0,3

Comments

Note that odd values for n>=65 are negative. - Vaclav Kotesovec, Jun 28 2013

Links

Table of n, a(n) for n=0..20.

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

Sequence in context: A088180 A370459 A206709 * A339079 A357361 A209111

Adjacent sequences: A199477 A199478 A199479 * A199481 A199482 A199483

Keyword

sign

Author

Vladimir Kruchinin, Nov 06 2011

Status

approved