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A347012
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E.g.f.: exp(x) / (1 - 4 * x)^(1/4).
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3
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1, 2, 8, 64, 800, 13376, 278272, 6914048, 199629824, 6566164480, 242327576576, 9915111636992, 445432721932288, 21795710738038784, 1153805878313615360, 65700181140859518976, 4004182878034473254912, 260071258357260225609728, 17932703649301871611346944
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(n,k) * A007696(k).
a(n) ~ n! * exp(1/4) * 4^n / (Gamma(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 14 2021
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MAPLE
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g:= proc(n) option remember; `if`(n<2, 1, (4*n-3)*g(n-1)) end:
a:= n-> add(binomial(n, k)*g(k), k=0..n):
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MATHEMATICA
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nmax = 18; CoefficientList[Series[Exp[x]/(1 - 4 x)^(1/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] 4^k Pochhammer[1/4, k], {k, 0, n}], {n, 0, 18}]
Table[HypergeometricU[1/4, n + 5/4, 1/4]/Sqrt[2], {n, 0, 18}]
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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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