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A304659
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a(n) = n*(n + 1)*(16*n - 1)/6.
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2
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0, 5, 31, 94, 210, 395, 665, 1036, 1524, 2145, 2915, 3850, 4966, 6279, 7805, 9560, 11560, 13821, 16359, 19190, 22330, 25795, 29601, 33764, 38300, 43225, 48555, 54306, 60494, 67135, 74245, 81840, 89936, 98549, 107695, 117390, 127650, 138491, 149929, 161980, 174660, 187985
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OFFSET
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0,2
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LINKS
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FORMULA
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O.g.f.: x*(5 + 11*x)/(1 - x)^4.
E.g.f.: x*(30 + 63*x + 16*x^2)*exp(x)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
Also, this sequence is related to A076455 by the same type of recurrence:
A076455(n) = n*a(n) - Sum_{k = 0..n-1} a(k) for n > 0.
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MATHEMATICA
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Table[n (n + 1) (16 n - 1)/6, {n, 0, 50}]
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PROG
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(PARI) concat(0, Vec(x*(5 + 11*x) / (1 - x)^4 + O(x^40))) \\ Colin Barker, May 25 2018
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CROSSREFS
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First lower diagonal of the rectangular array in A213835.
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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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