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A162482 Expansion of (1/(1-x)^3)*M(x/(1-x)^3), M(x) the g.f. of Motzkin numbers A001006. 2
1, 4, 14, 53, 218, 945, 4235, 19441, 90947, 432030, 2078416, 10105435, 49578341, 245131321, 1220218293, 6110131376, 30756858405, 155547919269, 789965192900, 4027121386190, 20600180351659, 105707046807196, 543973305719611 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.: 1/((1-x)^3-x-x^2/((1-x)^3-x-x^2/((1-x)^3-x-x^2/((1-x)^3-x-x^2/(1-... (continued fraction);

a(n) = sum{k=0..n, C(n+2k+2,n-k)*A001006(k)}.

Conjecture: (n+2)*a(n) +4*(-2*n-1)*a(n-1) +18*(n-1)*a(n-2) +13*(-2*n+5)*a(n-3) +17*(n-4)*a(n-4) +3*(-2*n+11)*a(n-5) +(n-7)*a(n-6)=0. - R. J. Mathar, Feb 10 2015

MAPLE

A162482 := proc(n)

    add(binomial(n+2*k+2, n-k)*A001006(k), k=0..n) ;

end proc:

seq(A162482(n), n=0..40) ; # R. J. Mathar, Feb 10 2015

CROSSREFS

Cf. A162481.

Sequence in context: A017948 A214998 A112872 * A308555 A000651 A192247

Adjacent sequences:  A162479 A162480 A162481 * A162483 A162484 A162485

KEYWORD

nonn

AUTHOR

Paul Barry, Jul 04 2009

STATUS

approved

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)