A073774 - OEIS

A073774

Number of plane binary trees of size n+3 and height n.

0, 0, 0, 4, 68, 376, 1440, 4736, 14272, 40576, 110592, 291840, 750592, 1890304, 4677632, 11403264, 27443200, 65306624, 153878528, 359399424, 832831488, 1916272640, 4380950528, 9957277696, 22510829568, 50642026496, 113413980160

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..26.

Henry Bottomley and Antti Karttunen, Derivations of the formulas for the diagonals of A073345 & A073346.

FORMULA

a(n) = A073345(n+3, n).

a(n < 3) = 0, a(3) = 4, a(n) = 1/12 * 2^(n-1) * (2*n^3 + 9*n^2 - 23*n - 78) or a(n) = 2^(n-2) * |A073775(n-3)| from n >= 3 onward.

MAPLE

A073774 := n -> `if`((n < 3), 0, (2^(n-2))*abs(A073775(n-3)));

CROSSREFS

Cf. A014480, A073345, A073773, A073775.

Sequence in context: A083931 A133881 A272134 * A247735 A221336 A339787

Adjacent sequences: A073771 A073772 A073773 * A073775 A073776 A073777

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 11 2002

STATUS

approved