A272339 First differences of 1/p(n), reciprocal of the number p(n) of unrestricted partitions of n (negated numerator).

0, 1, 1, 2, 2, 4, 4, 7, 2, 1, 1, 3, 24, 34, 41, 5, 2, 8, 3, 137, 5, 35, 253, 64, 383, 239, 41, 177, 7, 1039, 619, 137, 26, 2167, 2573, 3094, 3660, 398, 94, 293, 115, 71, 917, 11914, 13959, 4106, 4799, 3217, 26252, 2791, 3247, 1262, 2302, 8032, 1329, 75547, 87331, 50533, 53, 134647

Offset: 0

Author

Jean-François Alcover, Apr 26 2016

Keywords

• nonn
• frac

Examples

			Fractions begin: 0, -1/2, -1/6, -2/15, -2/35, -4/77, -4/165, -7/330, ...
		

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, A084911, A272340 (denominators).

Programs

Mathematica

-(Table[1/PartitionsP[n], {n, 0, 60}] // Differences) // Numerator

PARI

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

Formula

a(n) / A272340(n) = 1/p(n+1) - 1/p(n).

Product_{p prime} (1 - Sum_{n>=1} (a(n)/A272340(n))/p^n) = A272169. - Amiram Eldar, Nov 03 2020