OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
FORMULA
Self-convolution yields A166990.
a(n) ~ c * 8^n / n^2, where c = 0.231776... - Vaclav Kotesovec, Nov 27 2017
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 57*x^4 + 300*x^5 + 1693*x^6 +...
log(A(x)^2) = 2*x + 10*x^2/2 + 56*x^3/3 + 346*x^4/4 + 2252*x^5/5 + 15184*x^6/6 + 104960*x^7/7 +...+ A000172(n)*x^n/n +...
MATHEMATICA
a[n_] := Sum[(Binomial[n, k])^3, {k, 0, n}]; f[x_] := Sum[a[n]*x^n/(2*n), {n, 1, 75}]; CoefficientList[Series[Exp[f[x]], {x, 0, 50}], x] (* G. C. Greubel, May 30 2016 *)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^3)/2*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 17 2009
STATUS
approved