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A178962
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Partial sums of number of functors of degree n from free Abelian groups to Abelian groups A007322.
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0
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1, 7, 46, 366, 3647, 44205, 630956, 10350572, 191704349, 3954598099, 89888942874, 2231742720730, 60083847852539, 1743321481158041, 54226970410827160, 1800062257926566488, 63512168752599139129, 2373501269897667585631
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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FORMULA
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a(n) = SUM[i=1..n]] SUM[r>=0,s>=0] binomial(r*s+i-1,i)/2^(r+s+2).
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EXAMPLE
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a(3) = 1 + 6 + 39 = 46.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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