A059980 -id:A059980 - cp's OEIS frontend

A059978 a(n) = binomial(n+2,n)^6.

1, 729, 46656, 1000000, 11390625, 85766121, 481890304, 2176782336, 8303765625, 27680640625, 82653950016, 225199600704, 567869252041, 1340095640625, 2985984000000, 6327518887936, 12827693806929, 25002110044521, 47045881000000, 85766121000000, 151939915084881

Offset: 0

Robert G. Wilson v, Mar 06 2001

Number of 6-dimensional cage assemblies.

Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.

T. D. Noe, Table of n, a(n) for n = 0..1000
Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review.
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A059827, A059860, A000217, A059977, A059980, A091043.

with (combinat):seq(mul(stirling2(n+1,n),k=1..6),n=1..18); # Zerinvary Lajos, Dec 14 2007

m = 6; Table[n^m (n + 1)^m/2^m, {n, 1, 24}]

G.f.: (x^10 + 716*x^9 + 37257*x^8 + 450048*x^7 + 1822014*x^6 +2864328*x^5 + 1822014*x^4 + 450048*x^3 + 37257*x^2 + 716*x + 1)/(1-x)^13. - Colin Barker, Jul 09 2012
G.f.: 6F5([3,3,3,3,3,3], [1,1,1,1,1], z). - Benedict W. J. Irwin, Mar 14 2016
a(n) = (1/16)*( 3*S(7,n+1) + 10*S(9,n+1) + 3*S(11,n+1) ), where S(r,n) = Sum_{k = 1..n} k^r. Cf. A059977 and A059980. - Peter Bala, Jul 02 2019
From Amiram Eldar, May 15 2022: (Start)
Sum_{n>=0} 1/a(n) = 2688*Pi^2 + 448*Pi^4/15 + 128*Pi^6/945 - 29568.
Sum_{n>=0} (-1)^n/a(n) = 29568 - 32256*log(2) - 5376*zeta(3) - 720*zeta(5). (End)

Better definition from Zerinvary Lajos, May 23 2006

A091480 Table of multigraphs (by antidiagonals) with n (>=1) nodes and k (>=0) edges. Each type of object labeled from its own label set.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 9, 6, 1, 0, 1, 27, 36, 10, 1, 0, 1, 81, 216, 100, 15, 1, 0, 1, 243, 1296, 1000, 225, 21, 1, 0, 1, 729, 7776, 10000, 3375, 441, 28, 1, 0, 1, 2187, 46656, 100000, 50625, 9261, 784, 36, 1, 0, 1, 6561, 279936, 1000000, 759375

Offset: 1

Christian G. Bower, Jan 13 2004

			1  0   0    0     0 ...
1  1   1    1     1 ...
1  3   9   27    81 ...
1  6  36  216  1296 ...
1 10 100 1000 10000 ...

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 114 (2.4.44).

Columns 0-8: A000012, A000217(n-1), A000537(n-1), A059827(n-1), A059977(n-1), A059860(n-1), A059978(n-1), A059979(n-1), A059980(n-1).
Rows 1-10: A000007, A000012, A000244, A000400, A011557, A001024, A009965, A009972, A009980, A009989.
Cf. A091478.

a(n, k) = binomial(n, 2)^k.

cp's OEIS Frontend

A059978 a(n) = binomial(n+2,n)^6.

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