%I #107 Jul 17 2023 21:46:20
%S -1,23,47,71,95,119,143,167,191,215,239,263,287,311,335,359,383,407,
%T 431,455,479,503,527,551,575,599,623,647,671,695,719,743,767,791,815,
%U 839,863,887,911,935,959,983,1007,1031,1055,1079,1103,1127,1151,1175,1199
%N a(n) = 24*n - 1.
%C a(n) is also the denominator of the finite algebraic formula for the number of partitions of n, if n >= 1. The formula is p(n) = Tr(n)/(24*n - 1), n >= 1. See theorem 1.1 of the Bruinier-Ono paper in the link. For the numerators see A183011.
%C It appears that a(n) is also the denominator of the coefficient of the third term in the n-th Bruinier-Ono "partition polynomial" H_n(x). See the Bruinier-Ono paper, chapter 5 "Examples". For the numerators see A183007. - _Omar E. Pol_, Jul 13 2011
%C Also exponents in the formula q^(-1) + q^23 + 2*q^47 + 3*q^71 + 5*q^95 + 7*q^119 + 11*q^143 + 15*q^167 + ... in which the coefficients are the partition numbers (see A000041, Example section). - _Omar E. Pol_, Feb 27 2013
%H G. C. Greubel, <a href="/A183010/b183010.txt">Table of n, a(n) for n = 0..10000</a>
%H J. H. Bruinier and K. Ono, <a href="https://uva.theopenscholar.com/files/ken-ono/files/134.pdf">Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms</a>
%H A. Dabholkar, S. Murthy, and D. Zagier, <a href="http://arxiv.org/abs/1208.4074">Quantum Black Holes, Wall Crossing, and Mock Modular Forms</a>, arXiv:1208.4074 [hep-th], 2012-2014, see p. 46.
%H H. Gupta, <a href="http://www.ams.org/mathscinet-getitem?mr=14365">Congruent properties of sigma(n)</a>, Math. Student 13 (1945) 25-29.
%H E. Larson and L. Rolen, <a href="http://arxiv.org/abs/1107.4114">Integrality properties of the CM-values of certain weak Maass forms</a>, arXiv:1107.4114 [math.NT], 2011.
%H K. Ono, <a href="https://uva.theopenscholar.com/files/ken-ono/files/131_8.pdf">Congruences for the Andrews spt-function</a>, (see 2.1 Producing modular forms)
%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/kstresc.php?wyd=10&tom=42&jez=en">Elementary Theory of numbers</a>, Monografie Mathematyczne, vol. 42 (1964) chapt 4, p. 168.
%H Leo Tavares, <a href="/A183010/a183010.jpg">Illustration: Star Pairs</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = A008606(n) - 1.
%F a(1)=23, a(2)=47, a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 23 2011
%F a(n) = A183011(n)/A000041(n). - _Omar E. Pol_, Jul 14 2011
%F 24 * A280098(n) = A000203(a(n)) if n>0. - _Michael Somos_, Dec 25 2016
%F E.g.f.: (24*x-1)*exp(x). - _G. C. Greubel_, Aug 14 2018
%F G.f.: (-1 + 25*x)/(1-x)^2. - _Wolfdieter Lang_, Dec 10 2021
%F a(n) = 2*A008594(n) - 1. - _Leo Tavares_, Jun 06 2023
%e G.f. = -1 + 23*x + 47*x^2 + 71*x^3 + 95*x^4 + 119*x^5 + 143*x^6 + 167*x^7 + ...
%t Range[23, 2000, 24] (* _Vladimir Joseph Stephan Orlovsky_, Jun 14 2011 *)
%t (24*Range[0,50])-1 (* _Harvey P. Dale_, Mar 28 2015 *)
%o (PARI) a(n)=24*n-1 \\ _Charles R Greathouse IV_, Jun 14 2011
%o (Magma) [24*n-1: n in [0..50]]; // _G. C. Greubel_, Aug 14 2018
%Y Cf. A000041, A000203, A008606, A134517 (subset of primes), A183009, A183011, A187206, A280097 (sum of divisors), A280098.
%Y Cf. A008594.
%K sign,easy
%O 0,2
%A _Omar E. Pol_, Jan 21 2011