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Paolo Xausa, <a href="/A372583/b372583_1.txt">Table of n, a(n) for n = 1..10000</a>
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Paolo Xausa, <a href="/A372583/b372583_1.txt">Table of n, a(n) for n = 1..10000</a>
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Paolo Xausa, <a href="/A372583/b372583_1.txt">Table of n, a(n) for n = 1..10000</a>
A372583[n_] := (3*n^5 + 5*n^3)/8; Array[A372583, 50] (* Paolo Xausa, May 25 2024 *)
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The first ten pentagonal numbers are 1, 5, 12, 22, 35, 51, 70, 92, 117, and 145. Taking them in groups, respectively, of 1, 2, 3, and 4, i.e., (1), (5, 12), (22, 35, 51), and (70, 92, 117, 145), and summing each group separately gives 1, 17, 108, 424.
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a(n) = (3*n^5 + 5*n^3)/8.
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