login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A227018
a(n) = floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n*(n + 1)*(n + 2)*(n + 3)/24.
1
1, 3, 9, 24, 51, 95, 164, 266, 407, 598, 850, 1174, 1582, 2087, 2706, 3452, 4342, 5395, 6628, 8060, 9714, 11609, 13768, 16215, 18975, 22072, 25534, 29388, 33662, 38387, 43591, 49307, 55568, 62407, 69858, 77957, 86740, 96245, 106511, 117577, 129482, 142270
OFFSET
1,2
COMMENTS
See A227012.
LINKS
FORMULA
Conjectured g.f.: (-1 + x - 3 x^2 - 2 x^3 + 2 x^4 - 2 x^5 - 3 x^6 + 2 x^8 - 5 x^9 - x^12 - x^13 - 4 x^14 + 4 x^15 - 4 x^16 - 2 x^17 + 2 x^18 - 2 x^19 - 4 x^20 + 4 x^21 - 4 x^22 - x^23 - x^24 + x^25 - 4 x^26 + x^27 - x^28 - 3 x^29 + 3 x^30 - 5 x^31 - x^34 - 2 x^35 + x^36 - 3 x^37 + 2 x^38 + 2 x^39 - 2 x^40 - 3 x^41 + 6 x^42 - 3 x^43 - 3 x^44 + 6 x^45 - 4 x^46 + x^47)/((-1 + x)^5 (1 + x) (1 + x^2) (1 - x + x^2) (1 + x + x^2) (1 - x^2 + x^4) (1 - x^3 + x^6) (1 + x^3 + x^6) (1 - x^6 + x^12)).
EXAMPLE
a(1) = [1/(1/1)] = 1;
a(2) = [4/(1/2 + 1/3 + 1/4 + 1/5)] = 3;
a(3) = [10/(1/6 + 1/7 + ... + 1/15)] = 9.
MATHEMATICA
Clear[g]; g[n_] := N[Binomial[n + # - 1, #] &[4], 100]; a = {1}; Do[
AppendTo[a, Floor[(#2 - #1 + 1)/(HarmonicNumber[#2] - HarmonicNumber[#1 - 1])] &[g[k - 1] + 1, g[k]]], {k, 2, 100}]; a
CROSSREFS
Sequence in context: A352640 A029530 A301740 * A244504 A085739 A245762
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 06 2013
STATUS
approved