A262784 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n * (x^n/n) / (1 + x^n) ).

1, 1, 1, 3, 7, 18, 51, 147, 431, 1295, 3954, 12219, 38174, 120373, 382559, 1224173, 3940964, 12754732, 41476011, 135446194, 444016332, 1460619970, 4819995330, 15951789030, 52932499724, 176073789065, 587010353666, 1961118581900, 6564548926877, 22013613082514, 73945428978360, 248781470115309

Offset: 0

Author

Paul D. Hanna, Oct 01 2015

Keywords

• nonn

Comments

Compare to: exp( Sum_{n>=1} (x^n/n)/(1+x^n) ) = Sum_{n>=0} x^(n*(n+1)/2).

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 18*x^5 + 51*x^6 + 147*x^7 +...
where
log(A(x)) = A(x)*x/(1+x) + A(x)^2*(x^2/2)/(1+x^2) + A(x)^3*(x^3/3)/(1+x^3) + A(x)^4*(x^4/4)/(1+x^4) + A(x)^5*(x^5/5)/(1+x^5) +...
explicitly,
log(A(x)) = x + x^2/2 + 7*x^3/3 + 17*x^4/4 + 56*x^5/5 + 187*x^6/6 + 617*x^7/7 + 2033*x^8/8 + 6811*x^9/9 + 22906*x^10/10 +...
		

Crossrefs

Cf. A145268.

Programs

PARI

{a(n) = local(A=1+x); for(i=1,n, A = exp( sum(k=1,n, A^k*x^k/k/(1+x^k +x*O(x^n)))));polcoeff(A,n)}
for(n=0,40,print1(a(n),", "))