A115328 E.g.f: exp(x/(1-3*x))/sqrt(1-9*x^2).

1, 1, 16, 100, 2116, 27556, 732736, 14776336, 476112400, 13013333776, 494512742656, 17019717246016, 747017670477376, 30923039616270400, 1542024562112889856, 74433082892402872576, 4161241771884669788416

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. A115327.

Programs

Mathematica

CoefficientList[Series[E^(x/(1-3*x))/Sqrt[1-9*x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

PARI

a(n)=local(m=3);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 A115327 which has e.g.f.: exp(x+3/2*x^2).

D-finite with recurrence: a(n) = (3*n-2)*a(n-1) - 27*(n-1)*(n-2)^2*a(n-3) + 3*(n-1)*(3*n-2)*a(n-2). - Vaclav Kotesovec, Jun 26 2013

a(n) ~ 1/2*exp(-1/6+2*sqrt(n/3)-n)*3^n*n^n. - Vaclav Kotesovec, Jun 26 2013