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A356282
a(n) = Sum_{k=0..n} binomial(3*n, n-k) * p(k), where p(k) is the partition function A000041.
3
1, 4, 23, 141, 888, 5675, 36602, 237563, 1548995, 10135554, 66504699, 437359454, 2881641263, 19016505326, 125664684700, 831400186740, 5506287269802, 36501297800013, 242167539749593, 1607851773270316, 10682384379036741, 71016046921543562, 472376627798814453
OFFSET
0,2
FORMULA
a(n) ~ c * 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n + 1)), where c = Sum_{j>=0} p(j)/2^j = A065446 = 3.4627466194550636115379573429...
MATHEMATICA
Table[Sum[PartitionsP[k]*Binomial[3*n, n-k], {k, 0, n}], {n, 0, 30}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(3*n, n-k)*numbpart(k)); \\ Michel Marcus, Aug 02 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 01 2022
STATUS
approved