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A342170
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Product of first n little Schröder numbers.
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4
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1, 1, 3, 33, 1485, 292545, 264168135, 1130375449665, 23503896724884345, 2422053053602606867905, 1256704025339194996874320395, 3326147448057830199712191898815585, 45398150793225628820115544929795174823365, 3225056167710201318911738099365978237877235350145
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Product_{k=1..n} A001003(k).
a(n) ~ c * (1 + sqrt(2))^(n*(n+2)) * exp(3*n/2) / (2^((7*n + 3)/4) * Pi^((2*n + 3)/4) * n^(3*n/2 + 3/2 + 9/(16*sqrt(2)))), where c = 0.89405100528141459535141257102427907468205556782800836208733677564241771912...
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MAPLE
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b:= proc(n) option remember; `if`(n<2, 1,
((6*n-3)*b(n-1)-(n-2)*b(n-2))/(n+1))
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
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MATHEMATICA
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Table[Product[Hypergeometric2F1[1-k, k+2, 2, -1], {k, 1, n}], {n, 0, 15}]
FoldList[Times, 1, Table[Hypergeometric2F1[1 - n, n + 2, 2, -1], {n, 1, 15}]]
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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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