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A202835 E.g.f.: exp(9*x/(1-2*x)) / sqrt(1-4*x^2). 7
1, 9, 121, 2025, 40401, 927369, 24000201, 689220009, 21710549025, 743187098889, 27441452694681, 1086166287819369, 45846179189949681, 2054407698719865225, 97357866191666622441, 4862830945258077841449, 255239441235423753980481, 14040944744510973314880009 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = A083886(n)^2, where the e.g.f. of A083886 is exp(3*x + x^2).

a(n) = ( Sum_{k=0..[n/2]} 3^(n-2*k) * n!/((n-2*k)!*k!) )^2.

a(n) ~ n^n*exp(3*sqrt(2*n)-9/4-n)*2^(n-1). - Vaclav Kotesovec, May 23 2013

D-finite with recurrence: a(n) = (2*n+7)*a(n-1) + 2*(n-1)*(2*n+7)*a(n-2) - 8*(n-1)*(n-2)^2*a(n-3). - Vaclav Kotesovec, May 23 2013

EXAMPLE

E.g.f.: A(x) = 1 + 9*x + 121*x^2/2! + 2025*x^3/3! + 40401*x^4/4! +...

where A(x) = 1 + 3^2*x + 11^2*x^2/2! + 45^2*x^3/3! + 201^2*x^4/4! + 963^2*x^5/5! +...+ A083886(n)^2*x^n/n! +...

MATHEMATICA

CoefficientList[Series[Exp[9*x/(1-2*x)]/Sqrt[1-4*x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, May 23 2013 *)

PROG

(PARI) {a(n)=n!*polcoeff(exp(9*x/(1-2*x)+x*O(x^n))/sqrt(1-4*x^2+x*O(x^n)), n)}

(PARI) {a(n)=n!^2*polcoeff(exp(3*x+x^2+x*O(x^n)), n)^2}

(PARI) {a(n)=sum(k=0, n\2, 3^(n-2*k)*n!/((n-2*k)!*k!))^2}

CROSSREFS

Cf. A083886, A202827, A202828, A202829, A202831, A202833, A202836.

Sequence in context: A046184 A084769 A246467 * A321847 A050353 A112941

Adjacent sequences:  A202832 A202833 A202834 * A202836 A202837 A202838

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 25 2011

STATUS

approved

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)