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A370058
a(n) = 4*(4*n+3)!/(3*n+4)!.
5
1, 4, 44, 840, 23256, 850080, 38750400, 2120489280, 135566323200, 9922550077440, 818544054182400, 75160674504115200, 7604312776752384000, 840608992488545280000, 100812386907863414784000, 13037431708092153922560000, 1808675231786149165350912000
OFFSET
0,2
FORMULA
E.g.f.: exp( Sum_{k>=1} binomial(4*k,k) * x^k/k ).
a(n) = A000142(n) * A002293(n+1).
D-finite with recurrence 3*(3*n+2)*(3*n+4)*(n+1)*a(n) -8*n*(4*n+1)*(2*n+1)*(4*n+3)*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)^(3/4))^4.
a(n) = 4 * Sum_{k=0..n} (3*n+4)^(k-1) * |Stirling1(n,k)|. (End)
PROG
(PARI) a(n) = 4*(4*n+3)!/(3*n+4)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 08 2024
STATUS
approved