A115332 E.g.f: exp(x/(1-5*x))/sqrt(1-25*x^2).

1, 1, 36, 256, 11236, 181476, 9461776, 251412736, 15256202256, 574194155536, 39891552832576, 1953973812658176, 153336819846991936, 9264773325882888256, 812060124489852846336, 58352827798669641650176

Offset: 0

Author

Paul D. Hanna, Jan 20 2006

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A115331.

Programs

Mathematica

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

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)

Formula

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

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

a(n) ~ 1/2*exp(2*sqrt(n/5)-n-1/10)*5^n*n^n. - Vaclav Kotesovec, Jun 26 2013