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A059860
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a(n) = binomial(n+1, 2)^5.
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8
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1, 243, 7776, 100000, 759375, 4084101, 17210368, 60466176, 184528125, 503284375, 1252332576, 2887174368, 6240321451, 12762815625, 24883200000, 46525874176, 83841135993, 146211169851, 247609900000, 408410100000, 657748550151, 1036579476493, 1601568101376
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OFFSET
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1,2
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COMMENTS
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Number of 5-dimensional cage assemblies.
See Chap. 61, "Hyperspace Prisons", of C. Pickover's book "Wonders of Numbers" for full explanation of "cage numbers."
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REFERENCES
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Clifford A. Pickover, Wonders of Numbers, Oxford University Press, 2001, p. 325.
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LINKS
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Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review.
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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FORMULA
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L(n) = ((n^m)(n + 1)^m)/(2^m) where m is the dimension.
G.f.: x * (x^8 +232*x^7 +5158*x^6+ 27664*x^5 +47290*x^4 +27664*x^3 +5158*x^2 +232*x +1) / (1-x)^11. - Colin Barker, Jun 28 2012
Sum_{n>=1} 1/a(n) = 4032 - 1120*Pi^2/3 - 32*Pi^4/9.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4480*log(2) + 720*zeta(3) + 60*zeta(5) - 4032. (End)
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MAPLE
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for n from 1 to 100 do printf(`%d, `, ((n^5)*(n + 1)^5)/(2^5) ) od:
with (combinat):seq(mul(stirling2(n+1, n), k=1..5), n=1..21); # Zerinvary Lajos, Dec 14 2007
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MATHEMATICA
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m = 5; Table[ ( (n^m)(n + 1)^m )/(2^m), {n, 1, 26} ]
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PROG
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(PARI) { for (n=1, 1000, write("b059860.txt", n, " ", (n*(n + 1)/2)^5); ) } \\ Harry J. Smith, Jun 29 2009
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Corrected the definition from binomial(n+2,2)^5 to binomial(n+1,2)^5. - Harry J. Smith, Jun 29 2009
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STATUS
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approved
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