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A245054
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Number of hybrid (n+1)-ary trees with n internal nodes.
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2
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1, 2, 11, 155, 3920, 148348, 7585749, 492007235, 38798085127, 3609589528430, 387451906370509, 47166300422957938, 6423902286587614629, 968148639856266236900, 159999832729471473179245, 28775750341340155354161817, 5595702924360902427922341048
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 1/(n^2+1) * Sum_{i=0..n} C(n^2+i,i) * C(n^2+i+1,n-i).
a(n) = [x^n] ((1+x)/(1-x-x^2))^(n^2+1) / (n^2+1).
a(n) ~ 2^(n-1/2) * exp(n+1/4) * n^(n-5/2) / sqrt(Pi). - Vaclav Kotesovec, Jul 11 2014
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MAPLE
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a:= n-> add(binomial(n^2+i, i)*binomial(n^2+i+1, n-i), i=0..n)/(n^2+1):
seq(a(n), n=0..20);
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MATHEMATICA
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Table[Sum[Binomial[n^2+i, i]*Binomial[n^2+i+1, n-i], {i, 0, n}]/(n^2+1), {n, 0, 20}] (* Vaclav Kotesovec, Jul 11 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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