A227018 Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n*(n + 1)*(n + 2)*(n + 3)/24.

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

Clark Kimberling, Table of n, a(n) for n = 1..97

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

Cf. A227012, A227016.

Sequence in context: A352640 A029530 A301740 * A244504 A085739 A245762

Adjacent sequences: A227015 A227016 A227017 * A227019 A227020 A227021

Keyword

nonn,easy

Author

Clark Kimberling, Jul 06 2013

Status

approved