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%I #20 Nov 29 2020 07:44:10
%S 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,
%T 177,7,1039,619,137,26,2167,2573,3094,3660,398,94,293,115,71,917,
%U 11914,13959,4106,4799,3217,26252,2791,3247,1262,2302,8032,1329,75547,87331,50533,53,134647
%N First differences of 1/p(n), reciprocal of the number p(n) of unrestricted partitions of n (negated numerator).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274.
%H Amiram Eldar, <a href="/A272339/b272339.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) / A272340(n) = 1/p(n+1) - 1/p(n).
%F Product_{p prime} (1 - Sum_{n>=1} (a(n)/A272340(n))/p^n) = A272169. - _Amiram Eldar_, Nov 03 2020
%e Fractions begin: 0, -1/2, -1/6, -2/15, -2/35, -4/77, -4/165, -7/330, ...
%t -(Table[1/PartitionsP[n], {n, 0, 60}] // Differences) // Numerator
%o (PARI) a(n) = -numerator(1/numbpart(n+1) - 1/numbpart(n)); \\ _Michel Marcus_, Nov 03 2020
%Y Cf. A000041, A084911, A272340 (denominators).
%K nonn,frac
%O 0,4
%A _Jean-François Alcover_, Apr 26 2016