A371079 a(n) = Sum_{k=0..n} 3^(n - k)*Pochhammer(k/3, n - k). Row sums of A371077.

1, 1, 2, 7, 42, 383, 4716, 72831, 1349302, 29123127, 717194888, 19837095511, 608717233346, 20518453925807, 753563361399012, 29948045451609743, 1280446573813600366, 58602977409168609351, 2858550564643752169312, 148037904246807129342247, 8111929349028033318115898

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Cf. A371077, A370982, A000522.

Sequence in context: A158840 A359717 A038052 * A066383 A011802 A007065

Adjacent sequences: A371076 A371077 A371078 * A371080 A371081 A371082

Keyword

nonn,easy

Author

Peter Luschny, Mar 12 2024

Status

approved