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A370057
a(n) = 3*(4*n+2)!/(3*n+3)!.
4
1, 3, 30, 546, 14688, 526680, 23680800, 1282554000, 81339793920, 5915366392320, 485415660038400, 44376781223174400, 4473125162795520000, 492902545595556096000, 58949616073242166272000, 7605168496387089788160000, 1052810955815818170875904000
OFFSET
0,2
FORMULA
E.g.f.: exp( 3/4 * Sum_{k>=1} binomial(4*k,k) * x^k/k ).
a(n) = A000142(n) * A006632(n+1).
D-finite with recurrence 3*(3*n+2)*(3*n+1)*(n+1)*a(n) -8*n*(4*n+1)*(2*n+1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Feb 22 2024
From Seiichi Manyama, Aug 31 2024: (Start)
E.g.f. satisfies A(x) = 1/(1 - x*A(x))^3.
a(n) = 3 * Sum_{k=0..n} (3*n+3)^(k-1) * |Stirling1(n,k)|. (End)
PROG
(PARI) a(n) = 3*(4*n+2)!/(3*n+3)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 08 2024
STATUS
approved