A243440 - OEIS

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A243440

O.g.f.: exp( Integral Sum_{n>=1} n! * n^(n-1) * x^(n-1) / Product_{k=1..n} (1 - k*x) dx ).

1, 1, 3, 25, 499, 18897, 1158175, 104287909, 12948389505, 2119204222647, 442024984454145, 114447363118335099, 36014003359662761889, 13536516384259740525435, 5989775500211255393302197, 3082008257212085146469317911, 1824650971940959528920159955650, 1231558332755627626667173051846452

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 25*x^3 + 499*x^4 + 18897*x^5 + 1158175*x^6 +...

The logarithmic derivative equals the series:

A'(x)/A(x) = 1/(1-x) + 2!*2*x/((1-x)*(1-2*x)) + 3!*3^2*x^2/((1-x)*(1-2*x)*(1-3*x)) + 4!*4^3*x^3/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) + 5!*5^4*x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)) +...

Explicitly, the logarithm of the o.g.f. begins:

log(A(x)) = x + 5*x^2/2 + 67*x^3/3 + 1889*x^4/4 + 91771*x^5/5 + 6828545*x^6/6 + 721578187*x^7/7 + 102730470449*x^8/8 +...

PROG

(PARI) {a(n)=polcoeff(exp(intformal(sum(m=1, n+1, m!*m^(m-1)*x^(m-1)/prod(k=1, m, 1-k*x+x*O(x^n))))), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A084784, A243435.

Sequence in context: A356404 A366778 A136173 * A306783 A003024 A224679

Adjacent sequences: A243437 A243438 A243439 * A243441 A243442 A243443

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 05 2014

STATUS

approved