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A255640 Number of n-node rooted trees with a forbidden limb of length 10. 2
1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1841, 4764, 12481, 32960, 87776, 235286, 634585, 1720432, 4686643, 12820514, 35205696, 97009449, 268152813, 743354197, 2066114863, 5756601111, 16075024226, 44982031393, 126114491755, 354219140948, 996572117396 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Any rootward 10-node path starting at a leaf contains the root or a branching node.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 2.95571752117840968931298175785458006908910495018670567... and c = 0.43989037737488741580897781267482681067388... . - Vaclav Kotesovec, Feb 28 2016

MAPLE

with(numtheory):

g:= proc(n) option remember; `if`(n=0, 1, add(add(d*(g(d-1)-

      `if`(d=10, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)

    end:

a:= n-> g(n-1):

seq(a(n), n=1..40);

CROSSREFS

Column k=10 of A255636.

Sequence in context: A292554 A318803 A318856 * A216403 A145548 A292555

Adjacent sequences:  A255637 A255638 A255639 * A255641 A255642 A255643

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2015

STATUS

approved

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Last modified October 17 14:31 EDT 2019. Contains 328114 sequences. (Running on oeis4.)