cp's OEIS Frontend

A076276 Number of + signs needed to write the partitions of n (A000041) as sums.

%I A076276 #39 Oct 02 2021 19:38:55
%S A076276 0,0,1,3,7,13,24,39,64,98,150,219,322,455,645,892,1232,1668,2259,3008,
%T A076276 4003,5260,6897,8951,11599,14893,19086,24284,30827,38888,48959,61293,
%U A076276 76578,95223,118152,145993,180037,221175,271186,331402,404208,491521
%N A076276 Number of + signs needed to write the partitions of n (A000041) as sums.
%C A076276 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
%C A076276 Also total number of parts that are not the largest part in all partitions of n. - _Omar E. Pol_, Apr 30 2012
%C A076276 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
%F A076276 a(n) = (Sum_{k=1..n} tau(k)*numbpart(n-k))-numbpart(n) = A006128(n)-A000041(n), n>0. - _Vladeta Jovovic_, Oct 06 2002
%F A076276 G.f.: sum(n>=1, (n-1) * x^n / prod(k=1,n, 1-x^k ) ). - _Joerg Arndt_, Apr 17 2011
%F A076276 a(n) = A006128(n-1) + A182699(n), n >= 1. - _Omar E. Pol_, Oct 30 2011
%e A076276 4=1+3=2+2=1+1+2=1+1+1+1, 7 + signs are needed, so a(4)=7.
%t A076276 a[0]=0; a[n_] := Sum[DivisorSigma[0, k]PartitionsP[n-k], {k, 1, n}]-PartitionsP[n]
%Y A076276 Cf. A001475, A248475.
%K A076276 nonn
%O A076276 0,4
%A A076276 _Floor van Lamoen_, Oct 04 2002
%E A076276 More terms from _Vladeta Jovovic_, _Robert G. Wilson v_, _Dean Hickerson_ and _Don Reble_, Oct 06 2002