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A157280
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a(n) arises in the normal ordering of n-th power of the operator (d/dx)(x(d/dx))^4
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2
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OFFSET
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1,2
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COMMENTS
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this sequence generates the fifth terms of the following sequences:
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LINKS
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FORMULA
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Sequence defined through the following hypergeometric-type generating function, in Maple notation:
exp(-1)*sum(hypergeom([k+1,k+1,k+1,k+1],[1,1,1,1],x)/k!,k=0..infinity)=sum(a(n)*x^n/(n!)^5,n=0..infinity),
which is itself an infinite sum of hypergeometric functions.
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MATHEMATICA
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nMax = 8; kMax = 50; seq0 = {}; seq = {1}; While[seq != seq0, seq0 = seq; seq = (1/E Sum[HypergeometricPFQ[{k+1, k+1, k+1, k+1}, {1, 1, 1, 1}, x]/k!, {k, 0, kMax}] + O[x]^(nMax+1) // CoefficientList[#, x]&) Range[0, nMax]!^5 // Round; kMax += 10; Print[kMax]]; A157280 = seq (* Jean-François Alcover, Nov 07 2016 *)
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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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