This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A030982 Number of noncrossing nonplanted bushes with n nodes, i.e., rooted noncrossing trees with n nodes and no nodes of degree 1. 1
 0, 1, 1, 7, 18, 80, 284, 1169, 4628, 19137, 79165, 333058, 1410608, 6029816, 25941384, 112315945, 488862888, 2138161043, 9391903131, 41414729419, 183264846010, 813564012660, 3622193670040, 16170171489820, 72364908958800, 324586284275500, 1458976377988636 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA a(n) = 5*Sum_{k=2..n} ((-1)^(n-k)*2^(n-k)*k*C(n,k)*C(3*k-2,k-2)/(2*k+1))/n. Recurrence: 2*n*(2*n+1)*a(n) = (n-1)*(11*n-12)*a(n-1) + 6*(9*n^2-21*n+8) * a(n-2) - 4*(n-3)*(11*n-56)*a(n-3) - 152*(n-4)*(n-3)*a(n-4). - Vaclav Kotesovec, Oct 24 2012 a(n) ~ 5*19^(n+1/2)/(27*sqrt(Pi)*4^(n+1)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012 a(n) = A030981(n) - A030980(n). - Andrew Howroyd, Nov 12 2017 MATHEMATICA Table[5*Sum[(-1)^(n-k)*2^(n-k)*k*Binomial[n, k]*Binomial[3*k-2, k-2]/ (2*k+1), {k, 2, n}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 24 2012 *) PROG (PARI) a(n) = 5*sum(k=2, n, (-1)^(n-k)*2^(n-k)*k*binomial(n, k)*binomial(3*k-2, k-2)/(2*k+1))/n; \\ Andrew Howroyd, Nov 12 2017 CROSSREFS Cf. A030980, A030981. Sequence in context: A019534 A024830 A262489 * A203381 A207158 A304992 Adjacent sequences:  A030979 A030980 A030981 * A030983 A030984 A030985 KEYWORD nonn,easy AUTHOR 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.

Last modified December 14 17:44 EST 2019. Contains 329979 sequences. (Running on oeis4.)