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A198305 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - n*x^d/d). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Forms the logarithmic derivative of A198304.

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

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 +...

PROG

(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)}

CROSSREFS

Cf. A198304 (exp), A198299.

Sequence in context: A011769 A087432 A135052 * A146597 A320734 A259812

Adjacent sequences:  A198302 A198303 A198304 * A198306 A198307 A198308

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 27 2012

STATUS

approved

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Last modified September 18 00:40 EDT 2021. Contains 347493 sequences. (Running on oeis4.)