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A202833 E.g.f.: exp(9*x/(1-x)) / sqrt(1-x^2). 8
1, 9, 100, 1296, 19044, 311364, 5588496, 108993600, 2291345424, 51585311376, 1236953249856, 31447331115264, 844332494760000, 23859653712215616, 707522071322329344, 21958125453144843264, 711555574637600891136, 24025060090437573945600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = A202834(n)^2, where the e.g.f. of A202834 is exp(3*x + x^2/2).

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

a(n) ~ n^n*exp(6*sqrt(n)-9/2-n)/2 * (1+15/(4*sqrt(n))). - Vaclav Kotesovec, May 23 2013

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

EXAMPLE

E.g.f.: A(x) = 1 + 9*x + 100*x^2/2! + 1296*x^3/3! + 19044*x^4/4! +...

where A(x) = 1 + 3^2*x + 10^2*x^2/2! + 36^2*x^3/3! + 138^2*x^4/4! +...+ A202834(n)^2*x^n/n! +...

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[((9x)/(1-x))]/Sqrt[1-x^2], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Apr 23 2012 *)

PROG

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

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

CROSSREFS

Cf. A202834, A202827, A202828, A202829, A202831, A202835, A202836.

Sequence in context: A092936 A056002 A060150 * A287039 A174509 A103461

Adjacent sequences:  A202830 A202831 A202832 * A202834 A202835 A202836

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 25 2011

STATUS

approved

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Last modified March 28 20:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)