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A257055
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a(n) = n*(n + 1)*(n^2 - n + 3)/6.
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3
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0, 1, 5, 18, 50, 115, 231, 420, 708, 1125, 1705, 2486, 3510, 4823, 6475, 8520, 11016, 14025, 17613, 21850, 26810, 32571, 39215, 46828, 55500, 65325, 76401, 88830, 102718, 118175, 135315, 154256, 175120, 198033, 223125, 250530, 280386, 312835, 348023, 386100
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OFFSET
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0,3
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COMMENTS
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After 0, this sequence is the 2nd diagonal of the square array in A080851.
For n > 2, a(n)-n is the 4th column of the triangular array in A208657.
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LINKS
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FORMULA
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G.f.: x*(1 + 3*x^2)/(1 - x)^5.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, May 27 2021
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MATHEMATICA
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Table[n (n + 1) (n^2 - n + 3)/6, {n, 40}]
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PROG
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(PARI) vector(40, n, n--; n*(n+1)*(n^2-n+3)/6)
(Magma) [n*(n+1)*(n^2-n+3)/6: n in [0..40]];
(Sage) [n*(n+1)*(n^2-n+3)/6 for n in (0..40)]
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CROSSREFS
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Cf. similar sequences listed in A256859.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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