A356269 - OEIS

%I #7 Aug 01 2022 14:24:25

%S 1,3,15,75,425,2189,12353,63833,346973,1805573,9565325,49069517,

%T 257289529,1307750129,6723491129,34024174649,172873744739,

%U 865954792079,4359881882579,21679061144579,108108834714719,534409071271199,2642716232918639,12975671796056639,63765647596939139

%N a(n) = Sum_{k=0..n} binomial(2*k, k) * p(k), where p(k) is the partition function A000041.

%F a(n) ~ binomial(2*n,n) * p(n) * 4/3.

%F a(n) ~ 2^(2*n) * exp(Pi*sqrt(2*n/3)) / (3^(3/2) * sqrt(Pi) * n^(3/2)).

%t Table[Sum[Binomial[2*k, k] * PartitionsP[k], {k, 0, n}], {n, 0, 30}]

%Y Cf. A000041, A006134, A032443, A218481, A286955, A356267, A356270.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 01 2022