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A055507
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Sum{k = 1 to n}[d(k)*d(n+1-k)], where d(k) is number of positive divisors of k.
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5
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1, 4, 8, 14, 20, 28, 37, 44, 58, 64, 80, 86, 108, 108, 136, 134, 169, 160, 198, 192, 236, 216, 276, 246, 310, 288, 348, 310, 400, 344, 433, 396, 474, 408, 544, 450, 564, 512, 614, 522, 688, 560, 716, 638, 756, 636, 860, 676, 859, 772, 926, 758, 1016, 804, 1032
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = number of ways to express n+1 as a*b+c*d in positive integers a, b, c, d. - David W. Wilson (davidwwilson(AT)comcast.net), Jun 16 2003
tau(n) (A000005) convolved with itself, treating this result as a sequence whose offset is 2 - Graeme McRae (g_m(AT)mcraefamily.com), Jun 06 2006
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REFERENCES
| Andrews, George E., Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130. See D_{0,0}.
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FORMULA
| G.f.: Sum_{i >= 1, j >= 1} x^(i+j-1)/(1-x^i)/(1-x^j). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 11 2001
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EXAMPLE
| a[4] = d(1)*d(4) +d(2)*d(3) +d(3)*d(2) +d(4)*d(1) = 1*3 +2*2 +2*2 +3*1 = 14
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MAPLE
| with(numtheory); D00:=n->add(tau(j)*tau(n-j), j=1..n-1);
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CROSSREFS
| Cf. A000385.
Sequence in context: A176949 A173522 A049420 * A121896 A173290 A131937
Adjacent sequences: A055504 A055505 A055506 * A055508 A055509 A055510
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KEYWORD
| easy,nonn
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AUTHOR
| Leroy Quet Jun 29 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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