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A349541
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E.g.f.: exp(x) * (BesselI(0,8*x) + BesselI(1,8*x)).
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1
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1, 5, 41, 301, 2513, 20181, 170745, 1423101, 12161441, 103344037, 889924553, 7650373325, 66271512433, 574065261173, 4996181205657, 43511277885597, 380108373809985, 3323551100483397, 29122753514303337, 255427680480306285, 2243831648555990289, 19728657265135701525
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k,floor(k/2)) * 4^k.
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MATHEMATICA
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nmax = 21; CoefficientList[Series[Exp[x] (BesselI[0, 8 x] + BesselI[1, 8 x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] Binomial[k, Floor[k/2]] 4^k, {k, 0, n}], {n, 0, 21}]
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(n, k) * binomial(k, k\2) * 4^k); \\ Michel Marcus, Nov 21 2021
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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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