A392747 - OEIS

%I #10 Feb 20 2026 12:56:15

%S 1,7,1716,1331453,2151119533,5938064541933,25001581180419574,

%T 149146087541448025113,1197001151269888963598710,

%U 12438152383638540661198890270,162463054412281434919873901126151,2605489905334911696096494773053052893,50333834408520079001698097784322059257809

%N a(n) = Sum_{k=0..n} Stirling2(n+3*k,2*k).

%H Vincenzo Librandi, <a href="/A392747/b392747.txt">Table of n, a(n) for n = 0..140</a>

%F a(n) ~ 2^(6*n-1) * n^(2*n - 1/2) / (sqrt(Pi*(1-w)) * exp(2*n) * w^(2*n) * (2-w)^(2*n)), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.406375739959959907676958...

%t Table[Sum[StirlingS2[n+3*k, 2*k], {k, 0, n}], {n, 0, 12}]

%o (Magma) [&+[StirlingSecond(n+3*k, 2*k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Feb 20 2026

%Y Cf. A229286, A392726, A392734.

%Y Cf. A226775.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 21 2026