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A351501
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a(n) = binomial(n^2 + n - 1, n) / (n^2 + n - 1).
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1
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1, 2, 15, 204, 4095, 109668, 3689595, 149846840, 7141879503, 391139588190, 24218296445200, 1673538279265020, 127715832778905150, 10670643284149377480, 968929726650218004435, 95024894699780159868144, 10011211830149283223044015
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OFFSET
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1,2
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COMMENTS
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Empirical: In the ring of symmetric functions over the fraction field Q(q, t), let s(n) denote the Schur function indexed by n. Then (up to sign) a(n) is the coefficient of s(1^n) in nabla^(n) s(n) with q=t=1, where nabla denotes the "nabla operator" on symmetric functions.
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LINKS
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FORMULA
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a(n) ~ c*exp(n-1/(6*n))*n^(n-5/2), where c = sqrt(e/(2*Pi)). - Stefano Spezia, May 04 2022
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MATHEMATICA
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Table[With[{c=n^2+n-1}, Binomial[c, n]/c], {n, 20}] (* Harvey P. Dale, Jan 01 2024 *)
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PROG
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(Sage) [binomial(n*n+n-1, n)/(n*n+n-1) for n in range(1, 29)]
(Python)
from math import comb
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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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