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 A059860 a(n) = binomial(n+1, 2)^5. 8
 1, 243, 7776, 100000, 759375, 4084101, 17210368, 60466176, 184528125, 503284375, 1252332576, 2887174368, 6240321451, 12762815625, 24883200000, 46525874176, 83841135993, 146211169851, 247609900000, 408410100000, 657748550151, 1036579476493, 1601568101376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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." REFERENCES Clifford A. Pickover, Wonders of Numbers, Oxford University Press, 2001, p. 325. LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 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). FORMULA 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 From Amiram Eldar, May 15 2022: (Start) 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) MAPLE 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 MATHEMATICA m = 5; Table[ ( (n^m)(n + 1)^m )/(2^m), {n, 1, 26} ] Table[Binomial[n+1, 2]^5, {n, 20}] (* Harvey P. Dale, May 04 2018 *) PROG (PARI) { for (n=1, 1000, write("b059860.txt", n, " ", (n*(n + 1)/2)^5); ) } \\ Harry J. Smith, Jun 29 2009 CROSSREFS Cf. A059827. Sequence in context: A224356 A016769 A224015 * A268975 A223207 A224313 Adjacent sequences: A059857 A059858 A059859 * A059861 A059862 A059863 KEYWORD easy,nonn AUTHOR Jason Earls, Feb 28 2001 EXTENSIONS More terms from James A. Sellers, Feb 28 2001 Better definition from Zerinvary Lajos, May 23 2006 Corrected the definition from binomial(n+2,2)^5 to binomial(n+1,2)^5. - Harry J. Smith, Jun 29 2009 STATUS approved

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Last modified December 9 18:33 EST 2023. Contains 367693 sequences. (Running on oeis4.)