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A103439
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a(n) = Sum_{i=0..n-1} Sum_{j=0..i} (i-j+1)^j.
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5
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0, 1, 3, 7, 16, 39, 105, 315, 1048, 3829, 15207, 65071, 297840, 1449755, 7468541, 40555747, 231335960, 1381989881, 8623700811, 56078446615, 379233142800, 2662013133295, 19362917622001, 145719550012299, 1133023004941272, 9090156910550109, 75161929739797519
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OFFSET
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0,3
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COMMENTS
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Antidiagonal sums of array A103438.
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LINKS
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FORMULA
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a(n+1) = Sum_{k=0..n} ((k+2)^(n-k) + k)/(k+1). - Paul Barry, Oct 01 2006
G.f.: (G(0)-1)/(1-x) where G(k) = 1 + x*(2*k*x-1)/(2*k*x+x-1 - x*(2*k*x+x-1)^2/(x*(2*k*x+x-1) + (2*k*x+2*x-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 26 2013
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MAPLE
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b:= proc(i) option remember; add((i-j+1)^j, j=0..i) end:
a:= proc(n) option remember; add(b(i), i=0..n-1) end:
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MATHEMATICA
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Join[{0}, Table[Sum[Sum[(i-j+1)^j, {j, 0, i}], {i, 0, n}], {n, 0, 30}]] (* Harvey P. Dale, Dec 03 2018 *)
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PROG
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(Magma) [0] cat [(&+[ (&+[ (k-j+1)^j : j in [0..k]]) : k in [0..n-1]]): n in [1..30]]; // G. C. Greubel, Jun 15 2021
(Sage) [sum(sum((k-j+1)^j for j in (0..k)) for k in (0..n-1)) for n in (0..30)] # G. C. Greubel, Jun 15 2021
(PARI) a(n) = sum(i=0, n-1, sum(j=0, i, (i-j+1)^j)); \\ Michel Marcus, Jun 15 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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