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A052857 A simple grammar. 1
0, 1, 2, 15, 184, 3145, 68976, 1846999, 58413440, 2130740721, 88061420800, 4066862460991, 207556068584448, 11600364266112505, 704664527894104064, 46226086991634882375, 3256882066245640093696, 245279323467051422886241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 825

FORMULA

E.g.f.: exp(RootOf(exp(_Z)*x*_Z+exp(_Z)*x-_Z))*x.

a(n) = (n-1)!*Sum_{k=1..n-1} n^k*binomial(n-2,k-1)/k!, a(1)=1. - Vladimir Kruchinin, May 10 2011

a(n) = n!*hypergeom([-n+2], [2], -n) for n>=2. - Peter Luschny, Apr 20 2016

a(n) ~ exp(n/phi - n) * phi^(2*n-2) * n^(n-1) / 5^(1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 01 2017

E.g.f. A(x) satisfies: A(x) = x*exp(A(x)/(1 - A(x))). - Ilya Gutkovskiy, Apr 04 2019

MAPLE

spec := [S, {C=Set(B), S=Prod(Z, C), B=Sequence(S, 1<= card)}, labeled]:

seq(combstruct[count](spec, size=n), n=0..20);

# Alternatively:

a := n -> `if`(n<2, n, n!*hypergeom([-n+2], [2], -n));

seq(simplify(a(n)), n=0..17); # Peter Luschny, Apr 20 2016

MATHEMATICA

Table[If[0 <= n <= 1, n, (n - 1)! Sum[(n^k Binomial[n - 2, k - 1])/k!, {k, n - 1}]], {n, 0, 12}] (* Michael De Vlieger, Apr 20 2016 *)

PROG

(Maxima)

a(n):=if n=1 then 1 else ((n-1)!*sum((n^k*binomial(n-2, k-1))/k!, k, 1, n-1)); \\ Vladimir Kruchinin, May 10 2011

CROSSREFS

Sequence in context: A208409 A196792 A210655 * A053492 A319834 A268420

Adjacent sequences:  A052854 A052855 A052856 * A052858 A052859 A052860

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

STATUS

approved

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Last modified November 28 20:57 EST 2020. Contains 338755 sequences. (Running on oeis4.)