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a(n) = Sum_{k=0..n} C(n,k)*3^[k*(k-1)/2].
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%I #7 Nov 27 2017 07:42:50

%S 1,2,6,40,860,63000,14714728,10562062112,22960880409360,

%T 150300904214651680,2955814683617734854752,

%U 174481716707875308905153664,30905247968182392588500030233024

%N a(n) = Sum_{k=0..n} C(n,k)*3^[k*(k-1)/2].

%H G. C. Greubel, <a href="/A135755/b135755.txt">Table of n, a(n) for n = 0..49</a>

%F a(n) ~ 3^(n*(n-1)/2). - _Vaclav Kotesovec_, Nov 27 2017

%t Table[Sum[Binomial[n, k]*3^(Binomial[k, 2]), {k,0,n}], {n,0,10}] (* _G. C. Greubel_, Nov 07 2016 *)

%o (PARI) {a(n)=sum(k=0,n,binomial(n,k)*3^(k*(k-1)/2))}

%Y Cf. variants: A006896, A135756.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 27 2007