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A356269
a(n) = Sum_{k=0..n} binomial(2*k, k) * p(k), where p(k) is the partition function A000041.
3
1, 3, 15, 75, 425, 2189, 12353, 63833, 346973, 1805573, 9565325, 49069517, 257289529, 1307750129, 6723491129, 34024174649, 172873744739, 865954792079, 4359881882579, 21679061144579, 108108834714719, 534409071271199, 2642716232918639, 12975671796056639, 63765647596939139
OFFSET
0,2
FORMULA
a(n) ~ binomial(2*n,n) * p(n) * 4/3.
a(n) ~ 2^(2*n) * exp(Pi*sqrt(2*n/3)) / (3^(3/2) * sqrt(Pi) * n^(3/2)).
MATHEMATICA
Table[Sum[Binomial[2*k, k] * PartitionsP[k], {k, 0, n}], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 01 2022
STATUS
approved