A178962 Partial sums of number of functors of degree n from free Abelian groups to Abelian groups A007322.

1, 7, 46, 366, 3647, 44205, 630956, 10350572, 191704349, 3954598099, 89888942874, 2231742720730, 60083847852539, 1743321481158041, 54226970410827160, 1800062257926566488, 63512168752599139129, 2373501269897667585631

Offset

1,2

Comments

Partial sums of partial sums of number of matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n (A120733). Partial sums of dimensions of the graded components of the Hopf algebra MQSym (Matrix quasi-symmetric functions). a(2) = 7 is the only prime through a(18).

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = SUM[i=1..n]] SUM[r>=0,s>=0] binomial(r*s+i-1,i)/2^(r+s+2).

Example

a(3) =  1 + 6 + 39 = 46.

Crossrefs

Cf. A007322, A120733.

Sequence in context: A072948 A332852 A356827 * A203267 A319601 A352693

Adjacent sequences: A178959 A178960 A178961 * A178963 A178964 A178965

Keyword

nonn

Author

Jonathan Vos Post, Dec 31 2010

Status

approved