A251684 G.f.: exp( Sum_{n>=1} A047863(n)*x^n/n ), where A047863(n) = Sum_{k=0..n} binomial(n, k) * (2^k)^(n-k).

1, 2, 5, 16, 69, 426, 3947, 55612, 1177747, 36816650, 1676270109, 110202314208, 10408422663015, 1407329003121294, 271801891072128621, 74846096423770137324, 29351301902680241116593, 16374214768286861089202358, 12985582377076992552497257703, 14629438237685095017820000611400

Offset: 0

Author

Paul D. Hanna, Feb 14 2015

Keywords

• nonn

Comments

Logarithmic derivative yields A047863, the number of labeled graphs with 2-colored nodes where black nodes are only connected to white nodes and vice versa.

Examples

			G.f.: A(x) = 1 + 2*x + 5*x^2 + 16*x^3 + 69*x^4 + 426*x^5 + 3947*x^6 +...
where the logarithmic derivative yields A047863:
A'(x)/A(x) = 2 + 6*x + 26*x^2 + 162*x^3 + 1442*x^4 + 18306*x^5 + 330626*x^6 + 8488962*x^7 + 309465602*x^8 +...+ A047863(n+1)*x^n +...
		

Crossrefs

Cf. A047863.

Programs

PARI

{A047863(n) = sum(k=0, n, binomial(n, k) * (2^k)^(n-k) )}
{a(n)=local(A);A=exp(sum(k=1,n+1, A047863(k)*x^k/k) +x*O(x^n)); polcoeff(A,n)}
for(n=0, 20, print1(a(n), ", "))