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A342111
a(n) = (-1)^n * Sum_{k=0..n} Stirling1(n,k) * Stirling1(n,n-k).
8
1, 0, 1, 12, 193, 3980, 100805, 3034920, 105994833, 4215106728, 188097696345, 9309515255700, 506149663220641, 29989851619249236, 1923467938147053389, 132771455705186298000, 9814431285244231295265, 773520674985391641371280, 64752473306596841023424945
OFFSET
0,4
LINKS
FORMULA
a(n) ~ c * d^n * (n-1)!, where
d = A238261 = 4.9108149645682558987515348052403521978987052817678471761394112...
c = 0.06903826111269387517867145566264007373042059749428879149076344304196548...
MATHEMATICA
Table[(-1)^n*Sum[StirlingS1[n, k]*StirlingS1[n, n-k], {k, 0, n}], {n, 0, 20}]
PROG
(PARI) a(n) = (-1)^n*sum(k=0, n, stirling(n, k, 1)*stirling(n, n-k, 1)); \\ Michel Marcus, Feb 28 2021
(Magma) [(&+[(-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jun 03 2021
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 28 2021
STATUS
approved