OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..962
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 730
FORMULA
G.f.: A(x) = exp(A(x)^4*x + A(x^2)^4*x^2/2 + A(x^3)^4*x^3/3 +...), A(0)=1; also, A(x)^4 = sum_{n=0..inf} A052763(n+1)x^n. - Paul D. Hanna, Jul 13 2006
a(n) ~ c * d^n / n^(3/2), where d = 11.069962877759326312419302623317740386289... (see d(4) in A242249, or A052763) and c = 0.131073637348549764379358468465557... . - Vaclav Kotesovec, Mar 28 2017
MAPLE
spec := [S, {S=Set(B), B=Prod(Z, S, S, S, S)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
# second Maple program:
b:= proc(n) option remember; add(a(i)*a(n-i), i=0..n) end:
g:= proc(n) option remember; add(b(i)*b(n-i), i=0..n) end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(
d*g(d-1), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..25); # Alois P. Heinz, Jan 24 2017
MATHEMATICA
b[n_] := b[n] = Sum[a[i]*a[n-i], {i, 0, n}];
g[n_] := g[n] = Sum[b[i]*b[n-i], {i, 0, n}];
a[n_] := a[n] = If[n==0, 1, Sum[DivisorSum[j, #*g[#-1]&]*a[n-j], {j, 1, n} ]/n];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 28 2017, after Alois P. Heinz *)
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); if(n==0, 1, for(i=1, n, A=exp(sum(k=1, n, subst(x*A^4, x, x^k+x*O(x^n))/k))); polcoeff(A, n, x))} \\ Paul D. Hanna, Jul 13 2006
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from Paul D. Hanna, Jul 13 2006
STATUS
approved