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A277339
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Exponential self-convolution of this sequence gives central binomial coefficients (A000984).
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1
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1, 1, 2, 4, 7, 11, 26, 92, 64, -1328, 2272, 86912, -157706, -7271042, 17815604, 853696664, -2615703541, -133125019397, 490820087366, 26636670621548, -114924854384183, -6653655394184683, 32904766004185814, 2029701686588972068, -11322597283993315976
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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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E.g.f.: exp(x)*sqrt(BesselI_0(2*x)).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, (
binomial(2*n, n)-add(a(k)*a(n-k)*
binomial(n, k), k=1..n-1))/2)
end:
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MATHEMATICA
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Table[SeriesCoefficient[Exp[x] Sqrt[BesselI[0, 2 x]], {x, 0, n}] n!, {n, 0, 25}]
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PROG
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(PARI) x = 'x + O('x^30); serlaplace(exp(x)*sqrt(besseli(0, 2*x))) \\ Michel Marcus, Oct 09 2016
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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