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A260984 Coefficients of the mock theta function chibar(q). 1
1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 14, 16, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 44, 48, 52, 56, 60, 64, 68, 74, 80, 84, 90, 96, 104, 110, 118, 126, 134, 144, 152, 162, 172, 184, 196, 208, 220, 234, 248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 17, 4th equation.

LINKS

Table of n, a(n) for n=0..60.

K. Bringmann, J. Dousse, J. Lovejoy, and K. Mahlburg, Overpartitions with restricted odd differences, Electron. J. Combin. 22 (2015), no.3, paper 3.17.

K. Bringmann and J. Lovejoy, Dyson's rank, overpartitions, and weak Maass forms, arXiv:0708.0692 [math.NT], 2007.

K. Bringmann and J. Lovejoy, Dyson's rank, overpartitions, and weak Maass forms, Int. Math. Res. Not. (2007), rnm063

FORMULA

G.f.: 1 + 2*Sum_{n >= 1} q^(n(n+1)/2)*(1+q)^2(1+q^2)^2...(1+q^(n-1))^2*(1+q^n)/((1+q^3)(1+q^6)...(1+q^(3*n)).

G.f.: -1 + 2*(1/(1-x) + x^6/((1-x)*(1-x^5)*(1-x^7)) + x^24/((1-x)*(1-x^5)*(1-x^7)*(1-x^11)*(1-x^13) + ...). [Ramanujan] - Michael Somos, Sep 13 2016

EXAMPLE

G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 4*x^6 + 4*x^7 + 4*x^8 + ...

MAPLE

N:= 200: # to get a(0) to a(N)

M:= floor((sqrt(1+8*N)-1)/2):

G:= 1 + 2*add(q^(n*(n+1)/2)*mul((1+q^i)^2, i=1..n-1)*(1+q^n)/mul(1+q^(3*i), i=1..n), n=1..M):

S:= series(G, q, N+1):

seq(coeff(S, q, j), j=0..N); # Robert Israel, Aug 06 2015

MATHEMATICA

a[ n_] := If[ n < 1, Boole[n == 0], 2 SeriesCoefficient[ Sum[ x^(6 k^2) QPochhammer[ x^3, x^6, k] / QPochhammer[ x, x^2, 3 k + 1], {k, 0, Sqrt[n/6]}], {x, 0, n}]]; (* Michael Somos, Sep 13 2016 *)

CROSSREFS

Sequence in context: A001300 A169718 A001306 * A108105 A063468 A010336

Adjacent sequences:  A260981 A260982 A260983 * A260985 A260986 A260987

KEYWORD

nonn

AUTHOR

Jeremy Lovejoy, Aug 06 2015

STATUS

approved

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Last modified August 18 16:13 EDT 2018. Contains 313833 sequences. (Running on oeis4.)