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A273652

Number of forests of labeled rooted trees of height at most 1, with n labels, two of which are used for root nodes and any root may contain >= 1 labels.

2, 9, 30, 90, 255, 693, 1820, 4644, 11565, 28215, 67650, 159822, 372827, 860265, 1966200, 4456584, 10027161, 22413483, 49807550, 110100690, 242221287, 530579709, 1157628180, 2516582700, 5452595525, 11777605983, 25367150970, 54492397974, 116769423795

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OFFSET

2,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).

FORMULA

E.g.f.: x^2/2! * Sum_{j=0..2} Stirling2(2,j)*exp(x)^j.

a(n) = C(n,2) * Sum_{j=0..2} Stirling2(2,j) * j^(n-2).

G.f.: x^2*(2 - 3*x)*(1 - 3*x + 3*x^2)/((1 - x)*(1 - 2*x))^3. - Andrew Howroyd, Oct 31 2025

MAPLE

a:= n-> binomial(n, 2)*add(Stirling2(2, j)*j^(n-2), j=0..2):