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A276232 E.g.f. W(x)^W(x), where W(x) = LambertW(-x)/(-x) and satisfies W(x)^(1/W(x)) = exp(x).

%I A276232 #9 Aug 26 2016 03:01:17
%S A276232 1,1,5,37,369,4641,70513,1256361,25689569,592998049,15254145441,
%T A276232 432741923769,13422771397489,451956633181041,16418360947494353,
%U A276232 640101032269166281,26659869619363530177,1181426235219348415041,55506506359841719631425,2756055067645593490566489,144211201693287134720633681,7931567651481815767204102801
%N A276232 E.g.f. W(x)^W(x), where W(x) = LambertW(-x)/(-x) and satisfies W(x)^(1/W(x)) = exp(x).
%H A276232 Vaclav Kotesovec, <a href="/A276232/b276232.txt">Table of n, a(n) for n = 0..384</a>
%F A276232 E.g.f.: exp( LambertW(-x)^2/x ).
%F A276232 a(n) ~ 2*exp(exp(1)+1)*n^(n-1). - _Vaclav Kotesovec_, Aug 26 2016
%e A276232 E.g.f.: A(x) = 1 + x + 5*x^2/2! + 37*x^3/3! + 369*x^4/4! + 4641*x^5/5! + 70513*x^6/6! + 1256361*x^7/7! + 25689569*x^8/8! + 592998049*x^9/9! + 15254145441*x^10/10! +...
%e A276232 such that A(x) = W(x)^W(x).
%e A276232 Define W(x) = LambertW(-x)/(-x), where
%e A276232 W(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 125*x^4/4! + 1296*x^5/5! + 16807*x^6/6! + 262144*x^7/7! + 4782969*x^8/8! + 100000000*x^9/9! +...+ (n+1)^(n-1)*x^n/n! +...
%e A276232 satisfies W(x) = exp(x)^W(x).
%t A276232 CoefficientList[Series[E^(LambertW[-x]^2/x), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Aug 26 2016 *)
%o A276232 (PARI) {a(n) = my(A=1+x, W); W=serreverse(x*exp(-x +x^2*O(x^n)))/x; A = W^W; n!*polcoeff(A,n)}
%o A276232 for(n=0, 40, print1(a(n), ", "))
%Y A276232 Cf. A276231.
%K A276232 nonn
%O A276232 0,3
%A A276232 _Paul D. Hanna_, Aug 24 2016