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%I #9 Mar 14 2014 14:36:11
%S 1,6,67,1090,23265,614302,19323163,705288522,29296813825,
%T 1364468928022,70414831288275,3987980655931570,245910243177940897,
%U 16399345182278307822,1176033825828643912747,90242683036826223141370,7377887848681408224106497,640225878087732419052020134
%N E.g.f.: exp((1-5*x)^(-1/5)-1)/(1-5*x).
%C Generally, for e.g.f.: exp((1-p*x)^(-1/p)-1)/(1-p*x)), and p>1, we have a(n) ~ 1/sqrt(p+1) * p^(n+(2*p+1)/(2*p+2)) * exp((p+1)*p^(-p/(p+1)) *n^(1/(p+1))-n-1) * n^(n+p/(2*p+2)).
%F a(n) = 5*(6*n - 13)*a(n-1) - 5*(75*n^2 - 400*n + 557)*a(n-2) + 50*(50*n^3 - 475*n^2 + 1539*n - 1698)*a(n-3) - (9375*n^4 - 137500*n^3 + 764625*n^2 - 1910000*n + 1807524)*a(n-4) + (18750*n^5 - 390625*n^4 + 3267500*n^3 - 13716875*n^2 + 28896490*n - 24436079)*a(n-5) - 25*(n-5)^2*(5*n - 24)*(5*n - 23)*(5*n - 22)*(5*n - 21)*a(n-6).
%F a(n) ~ 1/sqrt(6) * 5^(n+11/12) * exp(6*5^(-5/6)*n^(1/6)-n-1) * n^(n+5/12).
%t CoefficientList[Series[E^((1-5*x)^(-1/5)-1)/(1-5*x),{x,0,20}],x]*Range[0,20]!
%Y Cf. A121629, A121630, A121631.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 14 2014
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