A115330 E.g.f: exp(x/(1-4*x))/sqrt(1-16*x^2).

1, 1, 25, 169, 5329, 78961, 3031081, 71995225, 3275616289, 108078535009, 5707994717881, 241468632426121, 14559189135946225, 750901957984356049, 50993055118129961929, 3098872535897951163961, 234376094007794247481921

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. A115329.

Programs

Mathematica

CoefficientList[Series[E^(x/(1-4*x))/Sqrt[1-16*x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

PARI

a(n)=local(m=4);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 A115329 which has e.g.f.: exp(x+2*x^2).

D-finite with recurrence: a(n) = (4*n-3)*a(n-1) + 4*(n-1)*(4*n-3)*a(n-2) - 64*(n-1)*(n-2)^2*a(n-3). - Vaclav Kotesovec, Jun 26 2013

a(n) ~ 2^(2*n-1)*n^n*exp(sqrt(n)-n-1/8) * (1 + 25/(96*sqrt(n))). - Vaclav Kotesovec, Jun 26 2013