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A371079
a(n) = Sum_{k=0..n} 3^(n - k)*Pochhammer(k/3, n - k). Row sums of A371077.
2
1, 1, 2, 7, 42, 383, 4716, 72831, 1349302, 29123127, 717194888, 19837095511, 608717233346, 20518453925807, 753563361399012, 29948045451609743, 1280446573813600366, 58602977409168609351, 2858550564643752169312, 148037904246807129342247, 8111929349028033318115898
OFFSET
0,3
FORMULA
From Vaclav Kotesovec, Mar 12 2024: (Start)
Recurrence: (n-6)*(3*n - 14)*a(n) = (27*n^3 - 375*n^2 + 1690*n - 2465)*a(n-1) - (81*n^4 - 1458*n^3 + 9726*n^2 - 28519*n + 31035)*a(n-2) + (81*n^5 - 1836*n^4 + 16542*n^3 - 74055*n^2 + 164751*n - 145753)*a(n-3) - (81*n^5 - 1998*n^4 + 19557*n^3 - 94944*n^2 + 228592*n - 218342)*a(n-4) - 2*(3*n - 11)*(9*n^3 - 129*n^2 + 611*n - 957)*a(n-5) + 2*(n-5)*(3*n - 16)*(3*n - 14)*(3*n - 11)*a(n-6).
a(n) ~ sqrt(2*Pi) * 3^(n-1) * n^(n - 7/6) / (Gamma(1/3) * exp(n)) * (1 + Gamma(1/3)^2 / (2*Pi*sqrt(3)*n^(2/3))). (End)
MAPLE
a := n -> local k; add(3^(n - k)*pochhammer(k/3, n - k), k = 0..n):
seq(a(n), n = 0..20);
MATHEMATICA
Table[Sum[3^(n-k) * Pochhammer[k/3, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Mar 12 2024
STATUS
approved