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A331501 Decimal expansion of exp(3/4). 2
2, 1, 1, 7, 0, 0, 0, 0, 1, 6, 6, 1, 2, 6, 7, 4, 6, 6, 8, 5, 4, 5, 3, 6, 9, 8, 1, 9, 8, 3, 7, 0, 9, 5, 6, 1, 0, 1, 3, 4, 4, 9, 1, 5, 8, 4, 7, 0, 2, 4, 0, 3, 4, 2, 1, 7, 7, 9, 1, 3, 3, 0, 3, 0, 8, 1, 0, 9, 8, 4, 5, 3, 3, 3, 6, 4, 0, 1, 2, 8, 2, 0, 0, 0, 2, 7, 9, 1, 5, 6, 0, 2, 6, 6, 6, 1, 5, 7, 9, 8, 2, 1, 8, 8, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Considering graph evolutions (see the Flajolet link) with 2n vertices initially isolated, the probability of the occurrence of an acyclic graph at the critical point n in the uniform model, will be denoted by P(n). In the case of the permutation model, the respective probability will be denoted by Pp(n).

Pp(n) / P(n) ~ exp(3/4) since Pp(n) = A302112(n) / A331505(2n) = A302112(n) / C(C(2n,2), n), and P(n) = A302112(n) * n! * 2^n / (2n)^(2n), Pp(n) / P(n) = (2n)^(2n) / (C(C(2n,2), n) * n! * 2^n), and Lim_{n->oo} Pp(n) / P(n) = exp(3/4).

LINKS

Table of n, a(n) for n=1..105.

P. Flajolet, D. E. Knuth, and B. Pittel, The first cycles in an evolving graph, Discrete Mathematics, 75(1-3):167-215, 1989.

FORMULA

Equals Lim_{n->oo} Pp(n) / P(n) =

Lim_{n->oo} (2*n)^(2*n) / (binomial(binomial(2n,2), n) * n! * 2^n).

EXAMPLE

2.1170000166126746685453698198370956101344915847024...

MAPLE

evalf(exp(3/4), 134);

CROSSREFS

Cf.  A001113, A019774, A092042, A302112, A331500, A331502, A331505.

Sequence in context: A214631 A025270 A249450 * A247450 A178234 A259175

Adjacent sequences:  A331498 A331499 A331500 * A331502 A331503 A331504

KEYWORD

nonn,cons

AUTHOR

Washington Bomfim, Feb 27 2020

STATUS

approved

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Last modified September 23 15:06 EDT 2020. Contains 337310 sequences. (Running on oeis4.)