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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

Index entries for sequences related to rooted trees

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

Emeric Deutsch

STATUS

approved

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