

A053275


Coefficients of the '7th order' mock theta function F_0(q)


5



1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1, 3, 2, 3, 3, 3, 2, 5, 3, 5, 4, 6, 5, 7, 5, 7, 7, 9, 7, 11, 9, 11, 11, 13, 12, 15, 13, 17, 16, 19, 17, 23, 21, 24, 23, 27, 26, 32, 29, 34, 34, 38, 37, 44, 42, 48, 48, 54, 52, 60, 58, 66, 67, 73, 72, 82, 81, 90, 90, 100, 99, 111, 110, 121, 123
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,8


COMMENTS

The rank of a partition is its largest part minus the number of parts.


REFERENCES

George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113134
Dean Hickerson, On the seventh order mock theta functions, Inventiones Mathematicae, 94 (1988) 661677
Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354355
Atle Selberg, Uber die MockThetafunktionen siebenter Ordnung, Arch. Math. Naturvidenskab, 41 (1938) 315


LINKS

Table of n, a(n) for n=0..76.


FORMULA

G.f.: F_0(q) = sum for n >= 0 of q^n^2/((1q^(n+1))(1q^(n+2))...(1q^(2n)))
a(n) = number of partitions of 7n with rank == 0 (mod 7) minus number with rank == 2 (mod 7)


MATHEMATICA

Series[Sum[q^n^2/Product[1q^k, {k, n+1, 2n}], {n, 0, 10}], {q, 0, 100}]


CROSSREFS

Other '7th order' mock theta functions are at A053276, A053277, A053278, A053279, A053280.
Sequence in context: A185318 A008622 A029414 * A025816 A025813 A161231
Adjacent sequences: A053272 A053273 A053274 * A053276 A053277 A053278


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson, Dec 19 1999


STATUS

approved



