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A197272
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a(n) = 6/((4*n+1)*(4*n+2))*binomial(5*n,n).
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2
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3, 1, 3, 15, 95, 690, 5481, 46376, 411255, 3781635, 35791910, 346821930, 3427001253, 34425730640, 350732771160, 3617153918640, 37703805776935, 396716804816265, 4209161209968825, 44993046668984145, 484176486362971710
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OFFSET
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0,1
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COMMENTS
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A combinatorial interpretation for this sequence in terms of a family of plane trees is given in [Schaeffer, Corollary 2 with k = 5].
A combinatorial interpretation for this sequence in terms of a family of four-dimensional stacked spheres is given in [Thorlieffson, Table 3 in Appendix B]. - Robert A. Russell, Mar 15 2012
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LINKS
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FORMULA
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a(n) = 6/((4*n+1)*(4*n+2))*binomial(5*n,n).
D-finite with recurrence 8*n*(4*n+1)*(2*n+1)*(4*n-1)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Mar 29 2023
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MAPLE
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6/((4*n+1)*(4*n+2))*binomial(5*n, n)
end proc:
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MATHEMATICA
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Table[6/((4n+1)(4n+2)) Binomial[5n, n], {n, 0, 20}] (* Harvey P. Dale, Aug 08 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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