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A209200 G.f.: (1-4*x)^(-1/2) * (1-8*x)^(-1/4). 2
1, 4, 20, 112, 680, 4384, 29536, 205440, 1462368, 10587520, 77633920, 574845440, 4289409280, 32206976000, 243074083840, 1842511532032, 14018197145088, 106996519311360, 818973463721984, 6284217844736000, 48327723087278080, 372397083591557120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals the convolution of sequences A000984 and A004981.

The sequences A000984 and A004981 are related by the identity:

Sum_{n>=0} A000984(n)^3 *x^n = ( Sum_{n>=0} A004981(n)^2 *x^n )^2.

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} A000984(n-k)*A004981(k).

Recurrence: n*a(n) = 4*(3*n-2)*a(n-1) - 8*(4*n-5)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ Gamma(3/4)*8^n/(Pi*n^(3/4)). - Vaclav Kotesovec, Oct 20 2012

EXAMPLE

G.f.: A(x) = 1 + 4*x + 60*x^2 + 1200*x^3 + 27300*x^4 + 668304*x^5 +...

This sequence equals the convolution of the sequences:

A000984 = [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...], and

A004981 = [1, 2, 10, 60, 390, 2652, 18564, 132600, 961350, ...].

Related sequences:

A^2: [1, 8, 56, 384, 2656, 18688, 133888, 974848, 7194112, ...],

A^4: [1, 16, 176, 1664, 14592, 122880, 1011712, 8224768, ...].

MATHEMATICA

CoefficientList[Series[(1-4*x)^(-1/2)*(1-8*x)^(-1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

PROG

(PARI) {a(n)=polcoeff((1-4*x +x*O(x^n))^(-1/2)*(1-8*x +x*O(x^n))^(-1/4), n)}

(PARI) {A000984(n)=polcoeff((1-4*x +x*O(x^n))^(-1/2), n)}

{A004981(n)=polcoeff((1-8*x +x*O(x^n))^(-1/4), n)}

{a(n)=sum(k=0, n, A000984(n-k)*A004981(k))}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A000984, A004981.

Sequence in context: A081085 A212326 A192624 * A294119 A245375 A108447

Adjacent sequences:  A209197 A209198 A209199 * A209201 A209202 A209203

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 06 2012

STATUS

approved

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Last modified September 26 05:00 EDT 2020. Contains 337346 sequences. (Running on oeis4.)