A166894 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * x^k] * x^n/n ), an integer series in x.

1, 1, 2, 4, 14, 89, 1050, 28983, 2066217, 272159513, 56735786726, 23441305184736, 26635730598676118, 64099902414443754551, 241666593661232949435382, 1531373212165249576810266758, 24642808245610936988728333582900

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

G.f.: exp( Sum_{n>=1} A166895(n)*x^n/n ) where A166895(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 14*x^4 + 89*x^5 + 1050*x^6 +...
log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 39*x^4/4 + 366*x^5/5 + 5697*x^6/6 +...+ A166895(n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^m*x^k)*x^m/m)+x*O(x^n)), n)}
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m\2, binomial(m-k, k)^(m-k)*m/(m-k))*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A166895.

Sequence in context: A371674 A181080 A375630 * A232108 A339651 A032052

Adjacent sequences: A166891 A166892 A166893 * A166895 A166896 A166897

Keyword

nonn

Author

Paul D. Hanna, Nov 23 2009

Status

approved