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A115328
E.g.f: exp(x/(1-3*x))/sqrt(1-9*x^2).
1
1, 1, 16, 100, 2116, 27556, 732736, 14776336, 476112400, 13013333776, 494512742656, 17019717246016, 747017670477376, 30923039616270400, 1542024562112889856, 74433082892402872576, 4161241771884669788416
OFFSET
0,3
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.
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
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 *)
PROG
(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)
CROSSREFS
Cf. A115327.
Sequence in context: A091100 A061432 A376705 * A223767 A223774 A224155
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 20 2006
STATUS
approved