login
A166993
G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/(2*n) ), where A005260(n) = Sum_{k=0..n} C(n,k)^4.
5
1, 1, 5, 32, 266, 2499, 25765, 283084, 3264502, 39077898, 481942608, 6089941550, 78523226064, 1029859481949, 13704960309415, 184688556173542, 2516342539576510, 34617557176739174, 480336524752492608
OFFSET
0,3
LINKS
FORMULA
Self-convolution yields A166992.
a(n) ~ c * 16^n / n^(5/2), where c = 0.14011467789446087641913961305130549385534145578464604013551918158... - Vaclav Kotesovec, Nov 27 2017
EXAMPLE
G.f.: A(x) = 1 + x + 5*x^2 + 32*x^3 + 266*x^4 + 2499*x^5 + 25765*x^6 +...
log(A(x)) = x + 9*x^2/2 + 82*x^3/3 + 905*x^4/4 + 10626*x^5/5 + 131922*x^6/6 + 1697508*x^7/7 +...+ A005260(n)/2*x^n/n +...
MATHEMATICA
a[n_] := Sum[(Binomial[n, k])^4, {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)^4)/2*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 17 2009
STATUS
approved