A272340 First differences of 1/p(n), reciprocal of the number p(n) of unrestricted partitions of n (denominator).

1, 2, 6, 15, 35, 77, 165, 330, 165, 105, 168, 616, 7777, 13635, 23760, 3696, 2079, 10395, 5390, 307230, 15048, 132264, 1257510, 395325, 3083850, 2384844, 523740, 2797795, 140270, 25582260, 19171284, 5193078, 1227303, 124860330, 183209730, 267551691, 388968349, 51171505, 14750505

Offset: 0

Author

Jean-François Alcover, Apr 26 2016

Keywords

• nonn
• frac

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000041, A272339 (numerators).

Programs

Mathematica

Table[1/PartitionsP[n], {n, 0, 60}] // Differences // Denominator

PARI

a(n) = denominator(1/numbpart(n+1) - 1/numbpart(n)); \\ Michel Marcus, Nov 03 2020

Formula

A272339(n) / a(n) = 1/p(n+1) - 1/p(n).