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 A182967 E.g.f.: A(x) = Product_{n>=1} (1 + 4*x^n/n)^n. 3

%I #9 Oct 07 2020 08:15:58

%S 1,4,8,120,576,6240,75840,772800,11585280,163914240,2694558720,

%T 45947489280,876665180160,17329568256000,364677585592320,

%U 8306018798837760,195321474697789440,4892032896606535680

%N E.g.f.: A(x) = Product_{n>=1} (1 + 4*x^n/n)^n.

%H Vaclav Kotesovec, <a href="/A182967/b182967.txt">Table of n, a(n) for n = 0..436</a>

%e E.g.f.: A(x) = 1 + 4*x + 8*x^2/2! + 120*x^3/3! + 576*x^4/4! +...

%e A(x) = (1+4x)*(1+4x^2/2)^2*(1+4x^3/3)^3*(1+4x^4/4)^4*(1+4x^5/5)^5*...

%t With[{nn=20},CoefficientList[Series[Product[(1+4 x^n/n)^n,{n,nn}],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 11 2020 *)

%o (PARI) {a(n,k=4)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}

%Y Cf. A181541, A182965, A182966, A007838.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 19 2010

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Last modified December 11 02:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)