

A053277


Coefficients of the '7th order' mock theta function F_2(q)


5



1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 4, 6, 5, 7, 7, 8, 8, 10, 9, 11, 11, 13, 13, 16, 15, 17, 18, 21, 20, 23, 23, 27, 27, 31, 31, 35, 35, 39, 41, 45, 45, 51, 51, 57, 59, 64, 66, 73, 74, 81, 83, 91, 93, 102, 104, 113, 117, 126, 130, 141, 144, 156, 162, 174, 178, 192, 198, 212
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OFFSET

0,3


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..70.


FORMULA

G.f.: F_2(q) = sum for n >= 0 of q^(n(n+1))/((1q^(n+1))(1q^(n+2))...(1q^(2n+1)))
a(n) = number of partitions of 7n+2 with rank == 1 (mod 7) minus number with rank == 2 (mod 7)


MATHEMATICA

Series[Sum[q^(n^2+n)/Product[1q^k, {k, n+1, 2n+1}], {n, 0, 9}], {q, 0, 100}]


CROSSREFS

Other '7th order' mock theta functions are at A053275, A053276, A053278, A053279, A053280.
Sequence in context: A178697 A255065 A027349 * A078661 A029263 A097575
Adjacent sequences: A053274 A053275 A053276 * A053278 A053279 A053280


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson, Dec 19 1999


STATUS

approved



