The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A161799 G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^2)^3. 3
 1, 3, 12, 61, 345, 2085, 13182, 86106, 576543, 3936029, 27294390, 191722887, 1361291244, 9754412169, 70447946556, 512278417176, 3747570671685, 27561220671408, 203657352324178, 1511270129552163, 11257532921742528 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Vaclav Kotesovec, Recurrence FORMULA a(n) = Sum_{k=0..n} C(3*n-2*k+2,k)/(n-k+1) * C(n+k-1,n-k). Let A(x)^m = Sum_{n>=0} a(n,m)*x^n then a(n,m) = Sum_{k=0..n} C(3*n-2*k+3*m-1,k)*m/(n-k+m) * C(n+k-1,n-k). a(n) ~ c*d^n/(sqrt(Pi)*n^(3/2)), where d = 8.01957328653868383... is the root of the equation 3125 + 22356*d - 162432*d^2 - 361584*d^3 - 326592*d^4 + 46656*d^5 = 0 and c = 1.56703431595354192843152170651865561188... - Vaclav Kotesovec, Sep 18 2013 MAPLE A161799 := proc(n) local s, t ; s := 2 ; t := 3; add( binomial(t*n-(t-1)*(k-1), k) * binomial(n+(s-1)*k-1, n-k) /(n-k+1) , k=0..n) ; end proc: seq(A161799(n), n=0..40) ; # R. J. Mathar, May 12 2022 MATHEMATICA Table[Sum[Binomial[3*n-2*k+2, k]/(n-k+1)*Binomial[n+k-1, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 18 2013 *) PROG (PARI) {a(n, m=1)=sum(k=0, n, binomial(3*n-2*k+3*m-1, k)*m/(n-k+m)*binomial(n+k-1, n-k))} CROSSREFS Cf. A161797, A161798. Sequence in context: A348200 A218092 A192479 * A182970 A159925 A331607 Adjacent sequences: A161796 A161797 A161798 * A161800 A161801 A161802 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 19 2009 STATUS approved

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

Last modified August 4 17:39 EDT 2024. Contains 374923 sequences. (Running on oeis4.)