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A370054
a(n) = 2*(3*n+1)!/(2*n+2)!.
2
1, 2, 14, 180, 3432, 87360, 2790720, 107442720, 4845456000, 250637587200, 14631376032000, 951675588864000, 68257101465907200, 5352223511771136000, 455529588681155788800, 41824228767217408512000, 4120692998969056333824000, 433653882272457833226240000
OFFSET
0,2
FORMULA
E.g.f.: exp( 2/3 * Sum_{k>=1} binomial(3*k,k) * x^k/k ).
a(n) = A000142(n)*A006013(n). - Alois P. Heinz, Feb 08 2024
From Seiichi Manyama, Aug 31 2024: (Start)
E.g.f. satisfies A(x) = 1/(1 - x*A(x))^2.
a(n) = 2 * Sum_{k=0..n} (2*n+2)^(k-1) * |Stirling1(n,k)|. (End)
PROG
(PARI) a(n) = 2*(3*n+1)!/(2*n+2)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 08 2024
STATUS
approved