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A178962 Partial sums of number of functors of degree n from free Abelian groups to Abelian groups A007322. 0

%I

%S 1,7,46,366,3647,44205,630956,10350572,191704349,3954598099,

%T 89888942874,2231742720730,60083847852539,1743321481158041,

%U 54226970410827160,1800062257926566488,63512168752599139129,2373501269897667585631

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

%C 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).

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

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

%Y Cf. A007322, A120733.

%K nonn

%O 1,2

%A _Jonathan Vos Post_, Dec 31 2010

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Last modified September 17 07:51 EDT 2021. Contains 347478 sequences. (Running on oeis4.)