A115332 - OEIS

%I #9 Jan 30 2020 21:29:15

%S 1,1,36,256,11236,181476,9461776,251412736,15256202256,574194155536,

%T 39891552832576,1953973812658176,153336819846991936,

%U 9264773325882888256,812060124489852846336,58352827798669641650176

%N E.g.f: exp(x/(1-5*x))/sqrt(1-25*x^2).

%C Term-by-term square of sequence with e.g.f.: exp(x+m/2*x^2) is given by e.g.f.: exp(x/(1-m*x))/sqrt(1-m^2*x^2) for all m.

%F Equals term-by-term square of A115331 which has e.g.f.: exp(x+5/2*x^2).

%F D-finite with recurrence: a(n) = (5*n-4)*a(n-1) + 5*(n-1)*(5*n-4)*a(n-2) - 125*(n-1)*(n-2)^2*a(n-3). - _Vaclav Kotesovec_, Jun 26 2013

%F a(n) ~ 1/2*exp(2*sqrt(n/5)-n-1/10)*5^n*n^n. - _Vaclav Kotesovec_, Jun 26 2013

%t CoefficientList[Series[E^(x/(1-5*x))/Sqrt[1-25*x^2], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)

%o (PARI) a(n)=local(m=5);n!*polcoeff(exp(x/(1-m*x+x*O(x^n)))/sqrt(1-m^2*x^2+x*O(x^n)),n)

%Y Cf. A115331.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 20 2006