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A329533
First differences of A051924, or second differences of Central binomial coefficients A000984.
1
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
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 15 2019
STATUS
approved