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

0,1

Links

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

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

a(n) ~ 9 * 4^n / sqrt(Pi*n). - Amiram Eldar, Oct 17 2025

Mathematica

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

Prog

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

Crossrefs

Cf. A000984, A051924, A163771, A094796.

Sequence in context: A047107 A149040 A055989 * A390702 A102871 A371842

Adjacent sequences: A329530 A329531 A329532 * A329534 A329535 A329536

Keyword

nonn,easy

Author

M. F. Hasler, Nov 15 2019

Status

approved