A288001 Expansion of 1/((1-x)(1-x^3)(1-x^5) ... (1-x^19)).

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 75, 88, 102, 119, 138, 159, 184, 211, 242, 277, 316, 359, 409, 463, 524, 592, 667, 750, 843, 945, 1057, 1182, 1318, 1469, 1635, 1816, 2014, 2233, 2470, 2730, 3014, 3323, 3659, 4026

Offset

0,4

Comments

Number of partitions of n into odd parts less than or equal to 19.

Number of partitions (d1,d2,...,d10) of n such that 0 <= d1/1 <= d2/2 <= ... <= d10/10.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 1, -1, 1, -2, 2, -2, 2, -3, 3, -3, 4, -5, 5, -5, 6, -7, 7, -7, 8, -9, 10, -9, 11, -12, 12, -12, 13, -15, 15, -15, 16, -18, 17, -17, 18, -20, 19, -19, 20, -21, 21, -20, 21, -22, 22, -20, 22, -22, 21, -20, 21, -21, 20, -19, 19, -20, 18, -17, 17, -18, 16, -15, 15, -15, 13, -12, 12, -12, 11, -9, 10, -9, 8, -7, 7, -7, 6, -5, 5, -5, 4, -3, 3, -3, 2, -2, 2, -2, 1, -1, 1, -1, 1, 0, 1, -1).

Mathematica

CoefficientList[Series[1/Times@@Table[(1-x^exp), {exp, Range[1, 19, 2]}], {x, 0, 60}], x] (* Harvey P. Dale, Mar 08 2025 *)

Crossrefs

Cf. A259094.

Sequence in context: A034149 A034150 A347587 * A034321 A034320 A058703

Adjacent sequences: A287998 A287999 A288000 * A288002 A288003 A288004

Keyword

nonn,changed

Author

Seiichi Manyama, Jun 04 2017

Status

approved