cp's OEIS Frontend

A228340 Triangle read by rows: T(n,k) = (n-1)*T(n-1,k) + T(n-2,k), with T(n,n-1)=1, T(n,n-2)=n-2, for n >= 1, 0 <= k <= n-1.

%I A228340 #15 Feb 15 2020 11:57:40
%S A228340 1,0,1,1,1,1,3,4,2,1,13,17,9,3,1,68,89,47,16,4,1,421,551,291,99,25,5,
%T A228340 1,3015,3946,2084,709,179,36,6,1,24541,32119,16963,5771,1457,293,49,7,
%U A228340 1,223884,293017,154751,52648,13292,2673,447,64,8,1
%N A228340 Triangle read by rows: T(n,k) = (n-1)*T(n-1,k) + T(n-2,k), with T(n,n-1)=1, T(n,n-2)=n-2, for n >= 1, 0 <= k <= n-1.
%H A228340 Reinhard Zumkeller, <a href="/A228340/b228340.txt">Rows n = 1..120 of table, flattened</a>
%H A228340 C. Cannings, <a href="http://dx.doi.org/10.4236/am.2013.45105">The Stationary Distributions of a Class of Markov Chains</a>, Applied Mathematics, Vol. 4 No. 5, 2013, pp. 769-773.
%e A228340 Triangle begins:
%e A228340 1,
%e A228340 0,1,
%e A228340 1,1,1,
%e A228340 3,4,2,1,
%e A228340 13,17,9,3,1,
%e A228340 68,89,47,16,4,1,
%e A228340 421,551,291,99,25,5,1,
%e A228340 3015,3946,2084,709,179,36,6,1,
%e A228340 ...
%o A228340 (Haskell)
%o A228340 a228340 n k = a228340_tabl !! (n-1) !! k
%o A228340 a228340_row n = a228340_tabl !! (n-1)
%o A228340 a228340_tabl = map (reverse . fst) $ iterate f ([1], [1,0]) where
%o A228340    f (us, vs'@(_ : vs@(v : _))) = (vs', ws) where
%o A228340      ws = 1 : (v + 1) : zipWith (+) us (map (* (v + 2)) vs)
%o A228340 -- _Reinhard Zumkeller_, Aug 31 2013
%Y A228340 Diagonals give A058307, A058279, A228341. Row sums give A001040.
%K A228340 nonn,tabl,easy
%O A228340 1,7
%A A228340 _N. J. A. Sloane_, Aug 29 2013