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A034715
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Dirichlet convolution of triangular numbers with themselves.
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4
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1, 6, 12, 29, 30, 78, 56, 132, 126, 200, 132, 402, 182, 378, 420, 588, 306, 864, 380, 1050, 798, 902, 552, 1920, 875, 1248, 1296, 2002, 870, 2940, 992, 2592, 1914, 2108, 2100, 4635, 1406, 2622, 2652, 5080, 1722, 5628, 1892, 4818, 4860, 3818, 2256, 8856
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OFFSET
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1,2
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 1..1000
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FORMULA
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G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^k/(1 - x^k)^3. - Ilya Gutkovskiy, Oct 24 2018
From Vaclav Kotesovec, Feb 05 2019: (Start)
Dirichlet g.f.: ((zeta(s-1) + zeta(s-2))/2)^2.
Sum_{k=1..n} a(k) ~ n^3*(log(n)/12 + (6*gamma - 1 + Pi^2)/36), where gamma is the Euler-Mascheroni constant A001620. (End)
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MATHEMATICA
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Table[n/4*Sum[(n+d)*(d+1)/d, {d, Divisors[n]}], {n, 1, 50}] (* Vaclav Kotesovec, Feb 05 2019 *)
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PROG
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(Magma) A000217:=func<i | i*(i+1)/2>; [&+[A000217(d)*A000217(n div d): d in Divisors(n)]: n in [1..50]]; // Bruno Berselli, Feb 11 2014
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CROSSREFS
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Cf. A000217.
Sequence in context: A323652 A223346 A109510 * A294730 A079390 A124679
Adjacent sequences: A034712 A034713 A034714 * A034716 A034717 A034718
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman
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STATUS
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approved
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