A081094 4th differences of partition numbers A000041.

2, -2, 3, -4, 5, -5, 5, -5, 7, -9, 11, -10, 10, -10, 14, -16, 20, -19, 21, -19, 26, -28, 36, -31, 37, -33, 48, -46, 63, -52, 68, -53, 82, -70, 107, -78, 117, -82, 145, -104, 181, -113, 202, -113, 244, -141, 306, -149, 346, -146, 419, -171, 514, -171, 593, -152, 714, -169, 878, -143, 1017, -87, 1228, -64, 1497

Offset: 0

Author

N. J. A. Sloane, Apr 25 2003

Keywords

• sign

Comments

Comtet appears to say this is nonnegative, which is only true for n sufficiently large.

An explanation is given by Odlyzko. - Moshe Shmuel Newman, Jun 11 2006

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115.
• A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
• Almkvist, Gert, "On the differences of the partition function", Acta Arith., 61.2 (1992), 173-181.

Crossrefs

Cf. A000041, A002865, A053445, A072380, A081095.

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^4 / (144 * sqrt(3) * n^3). - Vaclav Kotesovec, Oct 06 2017