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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

%I

%S 1,1,5,32,266,2499,25765,283084,3264502,39077898,481942608,6089941550,

%T 78523226064,1029859481949,13704960309415,184688556173542,

%U 2516342539576510,34617557176739174,480336524752492608

%N 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.

%H G. C. Greubel, <a href="/A166993/b166993.txt">Table of n, a(n) for n = 0..500</a>

%F Self-convolution yields A166992.

%F a(n) ~ c * 16^n / n^(5/2), where c = 0.14011467789446087641913961305130549385534145578464604013551918158... - _Vaclav Kotesovec_, Nov 27 2017

%e G.f.: A(x) = 1 + x + 5*x^2 + 32*x^3 + 266*x^4 + 2499*x^5 + 25765*x^6 +...

%e 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 +...

%t 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 *)

%o (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)}

%Y Cf. A005260, A166991, A166992.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 17 2009

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Last modified October 20 02:06 EDT 2021. Contains 348099 sequences. (Running on oeis4.)