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A272339
First differences of 1/p(n), reciprocal of the number p(n) of unrestricted partitions of n (negated numerator).
3
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
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
KEYWORD
nonn,frac
AUTHOR
STATUS
approved