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 A178962 Partial sums of number of functors of degree n from free Abelian groups to Abelian groups A007322. 0
 1, 7, 46, 366, 3647, 44205, 630956, 10350572, 191704349, 3954598099, 89888942874, 2231742720730, 60083847852539, 1743321481158041, 54226970410827160, 1800062257926566488, 63512168752599139129, 2373501269897667585631 (list; graph; refs; listen; history; text; internal format)
 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 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: A067318 A072948 A332852 * A203267 A319601 A197754 Adjacent sequences:  A178959 A178960 A178961 * A178963 A178964 A178965 KEYWORD nonn AUTHOR Jonathan Vos Post, Dec 31 2010 STATUS approved

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Last modified July 30 16:50 EDT 2021. Contains 346359 sequences. (Running on oeis4.)