A329533 First differences of A051924, or second differences of Central binomial coefficients A000984.

3, 10, 36, 132, 490, 1836, 6930, 26312, 100386, 384540, 1478048, 5697720, 22019556, 85284920, 330961950, 1286562960, 5009003250, 19528599420, 76231136520, 297910080600, 1165429743660, 4563490674600, 17884841191620, 70148829799152, 275344923755700, 1081512966189656, 4250730282412320

Offset: 0

Author

M. F. Hasler, Nov 15 2019

Keywords

• nonn

Crossrefs

Cf. A000984, A051924, A163771, A094796.

Programs

Mathematica

Differences[#, 2] &@ Array[Binomial[2 #, #] &, 29, 0] (* Michael De Vlieger, Nov 15 2019 *)

PARI

C=vector(30,n,binomial(2*n--,n));C=C[^1]-C[^-1];C=C[^1]-C[^-1]

Formula

a(n) = A051924(n) - A051924(n-1) = A000984(n+2) - 2*A000984(n+1) + A000984(n).

a(n) = 3*(3*n+2)*(n+1)*binomial(2*n+4,n+2)/(4*(2*n+1)*(2*n+3)). - Alois P. Heinz, Sep 13 2024