OFFSET
0,3
COMMENTS
Previous name was: A simple grammar.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 754
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 13.40708747253774757978704707270263863994591470583713..., c = 0.07868285364894808762720738672045999... . - Vaclav Kotesovec, Feb 24 2015
From Ilya Gutkovskiy, Apr 13 2019: (Start)
G.f. A(x) satisfies: A(x) = x*exp(5*Sum_{k>=1} (-1)^(k+1)*A(x^k)/k).
G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} (1 + x^n)^(5*a(n)). (End)
MAPLE
spec := [S, {B=PowerSet(S), S=Prod(Z, B, B, B, B, B)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(5*a(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n=1, 1, b((n-1)$2)):
seq(a(n), n=0..25); # Alois P. Heinz, Feb 24 2015
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[5*a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]]; a[n_] := If[n==1, 1, b[n-1, n-1]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name from Vaclav Kotesovec, Feb 24 2015
STATUS
approved