OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..445
FORMULA
a(n) ~ c * n!, where constant c = A238214 / exp(1) = 0.669014536209527303065690569951975534726... - Vaclav Kotesovec, Feb 21 2014
a(0) = 1, a(1) = 1, a(n) = Sum_{0 < k < n} k * a(k) * a(n-k-1). - Vladimir Reshetnikov, May 17 2016
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 12*x^4 + 62*x^5 + 385*x^6 +...
A'(x) = 1 + 2*x + 9*x^2 + 48*x^3 + 310*x^4 + 2310*x^5 + 19467*x^6 +...
A(x)*A'(x) = 1 + 3*x + 12*x^2 + 62*x^3 + 385*x^4 + 2781*x^5 +...
MATHEMATICA
a[0] = 1; a[1] = 1; a[n_] := a[n] = Sum[k a[k] a[n-k-1], {k, 1, n-1}]; Table[a[n], {n, 0, 20}] (* Vladimir Reshetnikov, May 17 2016 *)
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x+x^2*deriv(A^2/2)); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 05 2008
STATUS
approved