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

0,4

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000041, A084911, A272340 (denominators).

Sequence in context: A033732 A033752 A059886 * A267261 A219027 A341949

Adjacent sequences: A272336 A272337 A272338 * A272340 A272341 A272342

Keyword

nonn,frac

Author

Jean-François Alcover, Apr 26 2016

Status

approved