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A202829 E.g.f.: exp(4*x/(1-3*x)) / sqrt(1-9*x^2). 8
1, 4, 49, 676, 13225, 293764, 7890481, 236359876, 8052729169, 300797402500, 12388985000401, 551925653637604, 26614517015830969, 1373655853915667716, 75803216516463190225, 4440662493517062816004, 275697752917311709134241, 18052104090118575573856516 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = A202830(n)^2, where the e.g.f. of A202830 is exp(2*x + 3*x^2/2).

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

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

D-finite with recurrence: a(n) = (3*n+1)*a(n-1) + 3*(n-1)*(3*n+1)*a(n-2) - 27*(n-1)*(n-2)^2*a(n-3). - Vaclav Kotesovec, May 23 2013

EXAMPLE

E.g.f.: A(x) = 1 + 4*x + 49*x^2/2! + 676*x^3/3! + 13225*x^4/4! + 293764*x^5/5! +...

were A(x) = 1 + 2^2*x + 7^2*x^2/2! + 26^2*x^3/3! + 115^2*x^4/4! + 542^2*x^5/5! +...+ A202830(n)^2*x^n/n! +...

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[(4x)/(1-3x)]/Sqrt[1-9x^2], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Mar 09 2012 *)

PROG

(PARI) {a(n)=n!*polcoeff(exp(4*x/(1-3*x)+x*O(x^n))/sqrt(1-9*x^2+x*O(x^n)), n)}

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

CROSSREFS

Cf. A202830, A202827, A202828, A202831, A202833, A202835, A202836.

Sequence in context: A189146 A086094 A055793 * A204233 A144656 A121275

Adjacent sequences:  A202826 A202827 A202828 * A202830 A202831 A202832

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 25 2011

STATUS

approved

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Last modified February 27 10:15 EST 2020. Contains 332304 sequences. (Running on oeis4.)