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A359647
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a(n) = [x^n] hypergeom([1/4, 3/4], [2], 64*x). The central terms of the Motzkin triangle A359364 without zeros.
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2
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1, 6, 140, 4620, 180180, 7759752, 356948592, 17210021400, 859544957700, 44123307828600, 2315270298060720, 123691561681243920, 6707888537328997200, 368417878127146461600, 20455964090297751153600, 1146556787261188952159280, 64797319609481605046295780
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OFFSET
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0,2
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COMMENTS
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Number of Motzkin paths of length 4n with exactly 2n horizontal steps: a(1) = 6: UDHH, UHDH, UHHD, HUDH, HUHD, HHUD. - Alois P. Heinz, Aug 02 2023
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LINKS
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FORMULA
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MAPLE
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ser := series(hypergeom([1/4, 3/4], [2], 64*x), x, 20):
seq(coeff(ser, x, n), n = 0..16);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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