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a(n) = (22^n - 1)/21.
0, 1, 23, 507, 11155, 245411, 5399043, 118778947, 2613136835, 57489010371, 1264758228163, 27824681019587, 612142982430915, 13467145613480131, 296277203496562883, 6518098476924383427, 143398166492336435395, 3154759662831401578691, 69404712582290834731203
Partial sums are in A014907. Also, the sequence is related to A014940 by A014940(n) = n*a(n) -sum(a(i), Sum_{i=0..n-1} a(i) for n > 0. [Bruno Berselli, Nov 06 2012]
E.g.f.: exp(x)*(exp(21*x) - 1)/21. - Elmo R. Oliveira, Aug 29 2024
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(MAGMAMagma) [n le 2 select n-1 else 23*Self(n-1) - 22*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
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a(n) = (22^n-1)/21.
Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724, ..., A218733, ..., A218743, ..., A218751, -A218734, A132469, A218736-A218753, A218752, A133853, A094028, A218723.
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Vincenzo Librandi, <a href="/A218725/b218725.txt">Table of n, a(n) for n = 0..700</a>
a(n) = 23*a(n-1) - 22*a(n-2). - Vincenzo Librandi, Nov 07 2012
LinearRecurrence[{23, -22}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
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