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Search: id:A069948
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| A069948 |
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Sum( (k+n)!^3 / (k+n)!*(k!^3)*exp(1)), k = 0 .. infinity. |
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1
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| 1, 5, 87, 2971, 163121, 12962661, 1395857215, 194634226067, 33990369362241, 7247035915622821, 1848636684656077991, 555005864462114884875, 193458213840943964983537, 77399534126148191747554181
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Integral representation as n-th moment of a positive function on a positive halfaxis (solution of the Stieltjes moment problem), in Maple notation: a(n)=int(x^n*2*BesselK(0,2*sqrt(x))*hypergeom([],[1,1],x)/exp(1), x=0..infinity), n=0,1... Special values of the hypergeometric function of type 2F2: a(n)=exp(-1)*GAMMA(n+1)^2*hypergeom([n+1, n+1], [1, 1], 1) . From Karol A. Penson (penson(AT)lptl.jussieu.fr) and G. H. E. Duchamp (gduchamp2(AT)free.fr) Jan 09 2007
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MATHEMATICA
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f[n_] := f[n] = Sum[(k + n)!^3/((k + n)!*(k!^3)*E), {k, 0, Infinity}]; Table[ f[n], {n, 0, 13}] (* or *)
Table[n!^2*HypergeometricPFQ[{n + 1, n + 1}, {1, 1}, 1]/Exp[1], {n, 0, 13}] - Robert G. Wilson v, Jan 11, 2007
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CROSSREFS
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Cf. A000110, A020556 & A069223.
Sequence in context: A018925 A140159 A073862 this_sequence A054954 A106971 A136618
Adjacent sequences: A069945 A069946 A069947 this_sequence A069949 A069950 A069951
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), May 02 2002
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EXTENSIONS
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More terms from Robert G. Wilson v, Jan 11, 2007
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