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A055104 Expansion of 1 + q/((1-q)*(1-q^2)) + q^2/((1-q)*(1-q^2)*(1-q^3)*(1-q^4)). 2

%I #11 Mar 11 2019 15:55:39

%S 1,1,2,3,4,6,8,10,13,16,20,24,29,34,41,47,55,63,73,82,94,105,119,132,

%T 148,163,182,199,220,240,264,286,313,338,368,396,429,460,497,531,571,

%U 609,653,694,742,787,839,888,944,997,1058,1115,1180,1242

%N Expansion of 1 + q/((1-q)*(1-q^2)) + q^2/((1-q)*(1-q^2)*(1-q^3)*(1-q^4)).

%C First 3 terms of a sum studied by Ramanujan.

%H Colin Barker, <a href="/A055104/b055104.txt">Table of n, a(n) for n = 0..1000</a>

%H G. E. Andrews, <a href="http://www.jstor.org/stable/2974472">Simplicity and surprise in Ramanujan's "Lost" Notebook</a>, Amer. Math. Monthly, 104 (No. 10, Dec. 1997), 918-925.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).

%t LinearRecurrence[{1,1,0,0,-2,0,0,1,1,-1},{1,1,2,3,4,6,8,10,13,16,20},60] (* _Harvey P. Dale_, Mar 11 2019 *)

%o (PARI) Vec((1 - x^4 + x^5 - x^9 + x^10) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)) + O(x^100)) \\ _Colin Barker_, Oct 02 2017

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Jun 14 2000

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)