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1
Number of plane partitions (or planar partitions) of n.
(Formerly M2566 N1016)
+10
279
1, 1, 3, 6, 13, 24, 48, 86, 160, 282, 500, 859, 1479, 2485, 4167, 6879, 11297, 18334, 29601, 47330, 75278, 118794, 186475, 290783, 451194, 696033, 1068745, 1632658, 2483234, 3759612, 5668963, 8512309, 12733429, 18974973, 28175955, 41691046, 61484961, 90379784, 132441995, 193487501, 281846923
Decimal expansion of zeta(11).
+10
42
1, 0, 0, 0, 4, 9, 4, 1, 8, 8, 6, 0, 4, 1, 1, 9, 4, 6, 4, 5, 5, 8, 7, 0, 2, 2, 8, 2, 5, 2, 6, 4, 6, 9, 9, 3, 6, 4, 6, 8, 6, 0, 6, 4, 3, 5, 7, 5, 8, 2, 0, 8, 6, 1, 7, 1, 1, 9, 1, 4, 1, 4, 3, 6, 1, 0, 0, 0, 5, 4, 0, 5, 9, 7, 9, 8, 2, 1, 9, 8, 1, 4, 7, 0, 2, 5, 9, 1, 8, 4, 3, 0, 2, 3, 5, 6, 0, 6, 2
Expansion of Product_{k>=1} (1 - x^k)^(-k^2).
+10
29
1, 1, 5, 14, 40, 101, 266, 649, 1593, 3765, 8813, 20168, 45649, 101591, 223654, 486046, 1045541, 2225167, 4692421, 9804734, 20318249, 41766843, 85218989, 172628766, 347338117, 694330731, 1379437080, 2724353422, 5350185097, 10449901555, 20304465729, 39254599832
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of (j->j^k).
+10
19
1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 6, 5, 1, 1, 9, 14, 13, 7, 1, 1, 17, 36, 40, 24, 11, 1, 1, 33, 98, 136, 101, 48, 15, 1, 1, 65, 276, 490, 477, 266, 86, 22, 1, 1, 129, 794, 1828, 2411, 1703, 649, 160, 30, 1, 1, 257, 2316, 6970, 12729, 11940, 5746, 1593, 282, 42, 1, 1, 513
Expansion of exp( Sum_{n>=1} -sigma_10(n)*x^n/n ) in powers of x.
+10
6
1, -1, -512, -19171, -111645, 8255899, 287477144, 3248973702, -56353404842, -2946880278857, -50078654012311, -24091665240825, 19437354184565824, 486126425619195338, 4607922953609319032, -63107867988829247005, -3101395214088243725145
Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k^9).
+10
6
1, 512, 19683, 393472, 1953125, 20155392, 40353607, 290936320, 581140575, 2000000000, 2357947691, 18064270080, 10604499373, 41322093568, 76886718750, 209122656384, 118587876497, 694262555136, 322687697779, 1792500000000, 1588560093162, 2414538435584, 1801152661463
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