A222032 Irregular triangle read by rows in which row n gives denominators of the coefficients of the partition class polynomial Hpart_n(x), n >= 1.

1, 1, 23, 1, 1, 1, 47, 1, 2209, 47, 1, 1, 71, 1, 5041, 71, 357911, 5041, 1, 1, 95, 1, 9025, 19, 857375, 361, 11875, 1, 1, 119, 1, 2023, 1, 240737, 14161, 200533921, 1685159, 4857223, 1, 1, 143, 1, 1573, 143, 2924207, 20449, 418161601, 2924207, 27217619

Offset

1,3

Comments

For more information see A222031.

Links

Table of n, a(n) for n=1..49.

A. V. Sutherland, Partition class polynomials, Hpart_n(x), for n = 1..770

Example

For n = 1 the first partition class polynomial Hpart_1(x) is x^3 - 23*x^2 + 3592/23*x - 419, so the denominators of the coefficients are 1, 1, 23, 1.
Triangle begins:
1, 1, 23, 1;
1, 1, 47, 1, 2209, 47;
1, 1, 71, 1, 5041, 71, 357911, 5041;
1, 1, 95, 1, 9025, 19, 857375, 361, 11875;
1, 1, 119, 1, 2023, 1, 240737, 14161, 200533921, 1685159, 4857223;
1, 1, 143, 1, 1573, 143, 2924207, 20449, 418161601, 2924207, 27217619;
1, 1, 167, 1, 27889, 167, 4657463, 27889, 777796321, 4657463, 129891985607, 777796321;

Crossrefs

Row n has length 1 + A188569(n). For numerators see A222031.

Cf. A000041, A183007, A183010, A183011, A187218, A188569, A220515.

Sequence in context: A191816 A040535 A040536 * A040532 A040531 A348750

Adjacent sequences: A222029 A222030 A222031 * A222033 A222034 A222035

Keyword

nonn,frac,tabf

Author

Omar E. Pol, Mar 04 2013

Status

approved