A059860 a(n) = binomial(n+1, 2)^5.
1, 243, 7776, 100000, 759375, 4084101, 17210368, 60466176, 184528125, 503284375, 1252332576, 2887174368, 6240321451, 12762815625, 24883200000, 46525874176, 83841135993, 146211169851, 247609900000, 408410100000, 657748550151, 1036579476493, 1601568101376
Offset: 1
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).
Crossrefs
Cf. A059827.
Programs
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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
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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 *) -
PARI
a(n) = { (n*(n + 1)/2)^5 } \\ Harry J. Smith, Jun 29 2009
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)
Extensions
More terms from James 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
Comments