0,4

Also, total number of parts in all partitions of n-1 plus the number of emergent parts of n, if n >= 1. Also, sum of largest parts of all partitions of n-1 plus the number of emergent parts of n, if n >= 1. - Omar E. Pol, Oct 30 2011

Also total number of parts that are not the largest part in all partitions of n. - Omar E. Pol, Apr 30 2012

Empirical: For n > 1, a(n) is the sum of the entries in the second column of the lower-triangular matrix of coefficients giving the expansion of degree-n complete homogeneous symmetric functions in the Schur basis of the algebra of symmetric functions. - John M. Campbell, Mar 18 2018

a(n) = (Sum_{k=1..n} tau(k)*numbpart(n-k))-numbpart(n) = A006128(n)-A000041(n), n>0. - Vladeta Jovovic, Oct 06 2002

G.f.: sum(n>=1, (n-1) * x^n / prod(k=1,n, 1-x^k ) ). - Joerg Arndt, Apr 17 2011

a(n) = A006128(n-1) + A182699(n), n >= 1. - Omar E. Pol, Oct 30 2011

4=1+3=2+2=1+1+2=1+1+1+1, 7 + signs are needed, so a(4)=7.

a[0]=0; a[n_] := Sum[DivisorSigma[0, k]PartitionsP[n-k], {k, 1, n}]-PartitionsP[n]

Cf. A001475, A248475.

Sequence in context: A232533 A061263 A156209 * A296558 A376707 A309051

Adjacent sequences: A076273 A076274 A076275 * A076277 A076278 A076279

Floor van Lamoen, Oct 04 2002

More terms from Vladeta Jovovic, Robert G. Wilson v, Dean Hickerson and Don Reble, Oct 06 2002

approved