A132807 a(n) = A000108(n) + A000079(n) - 1.

1, 2, 5, 12, 29, 73, 195, 556, 1685, 5373, 17819, 60833, 212107, 751091, 2690823, 9727612, 35423205, 129775861, 477900843, 1767787477, 6565168995, 24468364171, 91486757943, 343068002257, 1289920924539, 4861979955883, 18367420181015, 69533685133731, 263748220185815

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

a(n) = Catalan(n) + 2^n - 1.

G.f.: (1 - sqrt(1 - 4*x))/(2*x) + 1/(1 - 2*x) - 1/(1 - x). - Alois P. Heinz, Sep 24 2025

Example

a(3) = 12 = Catalan(3) + 2^3 - 1 = 5 + 8 = 1.

Mathematica

A132807[n_] := CatalanNumber[n] + 2^n - 1; Array[A132807, 50, 0] (* Paolo Xausa, Sep 24 2025 *)

Prog

(PARI) a(n) = binomial(2*n, n)/(n+1) + 2^n - 1 \\ Andrew Howroyd, Sep 24 2025

Crossrefs

Cf. A000108, A000079.

Sequence in context: A089372 A036671 A152171 * A261234 A368984 A324787

Adjacent sequences: A132804 A132805 A132806 * A132808 A132809 A132810

Keyword

nonn,easy

Author

Gary W. Adamson, Aug 31 2007

Extensions

a(10) onwards from Andrew Howroyd, Sep 24 2025

Status

approved