A230741 O.g.f.: Sum_{n>=0} x^n * (n + x)^n / (1 + n*x)^n.

1, 1, 4, 15, 73, 425, 2908, 22855, 202849, 2005929, 21864076, 260374631, 3363097609, 46823803585, 699001981588, 11137295369775, 188636060894593, 3384325253935025, 64113731067110644, 1278893092183672159, 26792685755013073801, 588160948075800731961, 13500922657476722741164

Offset

0,3

Comments

Compare to the identity:

Sum_{n>=0} n^n * x^n / (1 + n*x)^n = 1/2 + Sum_{n>=0} (n+1)!/2 * x^n.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Example

G.f.: A(x) = 1 + x + 4*x^2 + 15*x^3 + 73*x^4 + 425*x^5 + 2908*x^6 +...
where
A(x) = 1 + x*(1+x)/(1+x) + x^2*(2+x)^2/(1+2*x)^2 + x^3*(3+x)^3/(1+3*x)^3 + x^4*(4+x)^4/(1+4*x)^4 + x^5*(5+x)^5/(1+5*x)^5 +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(m+x)^m/(1+m*x+x*O(x^n))^m), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A340355 A356009 A307996 * A020082 A020037 A086365

Adjacent sequences: A230738 A230739 A230740 * A230742 A230743 A230744

Keyword

nonn

Author

Paul D. Hanna, Oct 28 2013

Status

approved