A342111 - OEIS

%I #15 Sep 08 2022 08:46:26

%S 1,0,1,12,193,3980,100805,3034920,105994833,4215106728,188097696345,

%T 9309515255700,506149663220641,29989851619249236,1923467938147053389,

%U 132771455705186298000,9814431285244231295265,773520674985391641371280,64752473306596841023424945

%N a(n) = (-1)^n * Sum_{k=0..n} Stirling1(n,k) * Stirling1(n,n-k).

%H G. C. Greubel, <a href="/A342111/b342111.txt">Table of n, a(n) for n = 0..350</a>

%F a(n) ~ c * d^n * (n-1)!, where

%F d = A238261 = 4.9108149645682558987515348052403521978987052817678471761394112...

%F c = 0.06903826111269387517867145566264007373042059749428879149076344304196548...

%t Table[(-1)^n*Sum[StirlingS1[n, k]*StirlingS1[n, n-k], {k, 0, n}], {n, 0, 20}]

%o (PARI) a(n) = (-1)^n*sum(k=0, n, stirling(n, k, 1)*stirling(n, n-k, 1)); \\ _Michel Marcus_, Feb 28 2021

%o (Magma) [(&+[(-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jun 03 2021

%o (Sage) [sum( stirling_number1(n, k)*stirling_number1(n, n-k) for k in (0..n) ) for n in (0..30)] # _G. C. Greubel_, Jun 03 2021

%Y Cf. A008275, A014322, A047796, A132393, A342110.

%Y Cf. A048994, A155826.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Feb 28 2021