login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225439 Expansion of 3*x/((1-(1-9*x)^(1/3))*(1-9*x)^(2/3)). 3
1, 3, 21, 162, 1305, 10773, 90342, 765936, 6546177, 56293380, 486451251, 4220183916, 36731240910, 320571837810, 2804298945840, 24580601689752, 215832643307217, 1898042178972285, 16714070686567620, 147360883148636850, 1300623629653125855 (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) = sum(k=0..n, C(k,n-k)*3^(k)*(-1)^(n-k)*C(n+k-1,n-1)), n>0, a(0)=1.

G.f.: A(x) = 1 + x*B'(x)/B(x), where B(x) = (1-(1-9*x)^(1/3))/(3*x) is the g.f. of A097188.

n*(n-1)*a(n) = 18*(n-1)^2*a(n-1) - 9*(3*n-5)*(3*n-4)*a(n-2). - Vaclav Kotesovec, May 22 2013

a(n) ~ 3^(2*n-1)/(GAMMA(2/3)*n^(1/3)). - Vaclav Kotesovec, May 22 2013

a(n) = (Gamma(n+2/3)/Gamma(2/3)+Gamma(n+1/3)/(Gamma(1/3)))*3^(2*n-1)/ Gamma(n+1)) for n > 0. - Peter Luschny, Jul 05 2013

MAPLE

A225439 := n -> `if`(n=0, 1, (GAMMA(n+2/3)/GAMMA(2/3)+GAMMA(n+1/3)/(GAMMA(1/3)))* 3^(2*n-1)/GAMMA(n+1)): seq(A225439(i), i=0..20); # Peter Luschny, Jul 05 2013

MATHEMATICA

Table[Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 22 2013 *)

PROG

(Maxima) a(n):=if n=0 then 1 else sum(binomial(k, n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1, n-1), k, 0, n);

(PARI) x='x+O('x^66); Vec(3*x/((1-(1-9*x)^(1/3))*(1-9*x)^(2/3))) \\ Joerg Arndt, May 08 2013

(PARI) {a(n)=local(B=(1-(1-9*x+x^2*O(x^n))^(1/3))/(3*x)); polcoeff(1+x*B'/B, n, x)} \\ Paul D. Hanna, May 08 2013

CROSSREFS

Cf. A025748, A097188.

Sequence in context: A189508 A074570 A136781 * A180400 A166696 A058194

Adjacent sequences:  A225436 A225437 A225438 * A225440 A225441 A225442

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, May 08 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 21:46 EDT 2019. Contains 328315 sequences. (Running on oeis4.)