A198305 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - n*x^d/d).

1, 3, 7, 19, 51, 159, 519, 1867, 7234, 30243, 135125, 642307, 3231047, 17138845, 95554662, 558384955, 3411049542, 21730279218, 144048688538, 991665854999, 7077433997172, 52283785492733, 399238054300828, 3147127294177099, 25579801627862301, 214139186144996635

Offset: 1

Author

Paul D. Hanna, Jan 27 2012

Keywords

• nonn

Comments

Forms the logarithmic derivative of A198304.

Examples

			L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 19*x^4/4 + 51*x^5/5 + 159*x^6/6 +...
such that, by definition:
L(x) = x/(1-x) + (x^2/2)/((1-2*x)*(1-x^2)) + (x^3/3)/((1-3*x)*(1-x^3)) + (x^4/4)/((1-4*x)*(1-2*x^2)*(1-x^4)) + (x^5/5)/((1-5*x)*(1-x^5)) + (x^6/6)/((1-6*x)*(1-3*x^2)*(1-2*x^3)*(1-x^6)) +...+ (x^n/n)/Product_{d|n} (1-n*x^d/d) +...
Exponentiation yields the g.f. of A198304:
exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 21*x^5 + 54*x^6 + 148*x^7 +...
		

Crossrefs

Cf. A198304 (exp), A198299.

Programs

PARI

{a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, -log(1-m*x^d/d+x*O(x^n))))), n)}