A239301 E.g.f.: exp((1-5*x)^(-1/5)-1)/(1-5*x).

1, 6, 67, 1090, 23265, 614302, 19323163, 705288522, 29296813825, 1364468928022, 70414831288275, 3987980655931570, 245910243177940897, 16399345182278307822, 1176033825828643912747, 90242683036826223141370, 7377887848681408224106497, 640225878087732419052020134

Offset: 0

Author

Vaclav Kotesovec, Mar 14 2014

Keywords

• nonn

Comments

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)).

Crossrefs

Cf. A121629, A121630, A121631.

Programs

Mathematica

CoefficientList[Series[E^((1-5*x)^(-1/5)-1)/(1-5*x),{x,0,20}],x]*Range[0,20]!

Formula

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).

a(n) ~ 1/sqrt(6) * 5^(n+11/12) * exp(6*5^(-5/6)*n^(1/6)-n-1) * n^(n+5/12).