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.

1, 1, 5, 32, 266, 2499, 25765, 283084, 3264502, 39077898, 481942608, 6089941550, 78523226064, 1029859481949, 13704960309415, 184688556173542, 2516342539576510, 34617557176739174, 480336524752492608

Offset: 0

Author

Paul D. Hanna, Nov 17 2009

Keywords

• nonn

Examples

			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 +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A005260, A166991, A166992.

Programs

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 *)

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)}

Formula

Self-convolution yields A166992.

a(n) ~ c * 16^n / n^(5/2), where c = 0.14011467789446087641913961305130549385534145578464604013551918158... - Vaclav Kotesovec, Nov 27 2017