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A006324
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n*(n + 1)*(2*n^2 + 2*n - 1)/6.
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4
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1, 11, 46, 130, 295, 581, 1036, 1716, 2685, 4015, 5786, 8086, 11011, 14665, 19160, 24616, 31161, 38931, 48070, 58730, 71071, 85261, 101476, 119900, 140725, 164151, 190386, 219646, 252155, 288145, 327856, 371536, 419441, 471835, 528990, 591186
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 4-dimensional analogue of centered polygonal numbers.
This sequence enabled the analysis of A162012 and A162013. [Johannes W. Meijer, Jun 27 2009]
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FORMULA
| 8*C(n + 2, 4) + C(n + 1, 2).
a(n) = Sum[k^5,{k,1,n}]/Sum[k,{k,1,n}] = A000539(n) / A000217(n). - Alexander Adamchuk, Apr 12 2006
Partial sums of A000447. - Zak Seidov
Contribution from Johannes W. Meijer, Jun 27 2009: (Start)
Recurrence relation sum((-1)^k*binomial(5,k)*a(n-k), k= 0 .. 5) = 0.
GF(z) = (1+6*z+z^2)/(1-z)^5.
(End)
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MATHEMATICA
| Table[Sum[k^5, {k, 1, n}]/Sum[k, {k, 1, n}], {n, 1, 40}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
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CROSSREFS
| Cf. A000447, A000539, A000217.
Contribution from Johannes W. Meijer, Jun 27 2009: (Start)
Equals the absolute values of the coefficients that precede the a(n-1) factors of the recurrence relations RR(n) of A162011.
Cf. A162012 [a(n-2)] and A162013 [a(n-3)].
(End)
Sequence in context: A081587 A143059 A155014 * A177370 A126672 A179786
Adjacent sequences: A006321 A006322 A006323 * A006325 A006326 A006327
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KEYWORD
| nonn,easy
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AUTHOR
| Albert Rich (Albert_Rich(AT)msn.com)
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EXTENSIONS
| Simpler definition from Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
More terms from Zak Seidov (zakseidov(AT)yahoo.com)
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