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A166992 G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/n ) where A005260(n) = Sum_{k=0..n} C(n,k)^4. 6

%I

%S 1,2,11,74,621,5850,60212,659712,7583514,90494068,1112755389,

%T 14022849582,180362150901,2360201899690,31344689243344,

%U 421621652965160,5734850816825046,78773961705345324,1091497852618784390

%N G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/n ) where A005260(n) = Sum_{k=0..n} C(n,k)^4.

%H G. C. Greubel, <a href="/A166992/b166992.txt">Table of n, a(n) for n = 0..500</a>

%F Self-convolution of A166993.

%F a(n) ~ c * 16^n / n^(5/2), where c = 0.30919827904959014083681667605470681109347914449671378054261267779... - _Vaclav Kotesovec_, Nov 27 2017

%e G.f.: A(x) = 1 + 2*x + 11*x^2 + 74*x^3 + 621*x^4 + 5850*x^5 + 60212*x^6 +...

%e log(A(x)) = 2*x + 18*x^2/2 + 164*x^3/3 + 1810*x^4/4 + 21252*x^5/5 + 263844*x^6/6 + 3395016*x^7/7 +...+ A005260(n)*x^n/n +...

%t a[n_] := Sum[(Binomial[n, k])^4, {k, 0, n}]; f[x_] := Sum[a[n]*x^n/(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)*x^m/m)+x*O(x^n)),n)}

%Y Cf. A005260, A166990, A166993.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 17 2009

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Last modified October 18 21:24 EDT 2021. Contains 348070 sequences. (Running on oeis4.)