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A015502
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a(1) = 1, a(n) = Sum_{k=1..n-1} (3^k - 1)/2 * a(k).
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11
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1, 1, 5, 70, 2870, 350140, 127801100, 139814403400, 458731057555400, 4514831068460246800, 133300387296288786770000, 11806948504381482999365980000, 3137354163532752044074527571580000, 2500979519710095684958538548015855960000
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) ~ c * 3^(n*(n-1)/2) / 2^(n+1), where c = A132323 = QPochhammer(-1, 1/3) = 3.129868... . - Vaclav Kotesovec, Mar 24 2017
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MATHEMATICA
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Flatten[{1, Table[QPochhammer[-1, 3, n]/2^(n+1), {n, 2, 15}]}] (* Vaclav Kotesovec, Mar 24 2017 *)
a[n_, m_]:= a[n, m]= If[n<3, 1, (m^(n-1)+m-2)*a[n-1, m]/(m-1)];
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PROG
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(Magma) [n le 2 select 1 else ((3^(n-1)+1)/2)*Self(n-1): n in [1..15]]; // Vincenzo Librandi, Nov 11 2012
(SageMath)
def a(n, m): return 1 if (n<3) else (m^(n-1) + m-2)*a(n-1, m)/(m-1)
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CROSSREFS
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Sequences with the recurrence a(n) = (m^(n-1) + m-2)*a(n-1)/(m-1): A036442 (m=2), this sequence (m=3), A015503 (m=4), A015506 (m=5), A015507 (m=6), A015508 (m=7), A015509 (m=8), A015511 (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).
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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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