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A recursive triangle sequence: A(n,k)=k^2*(A(n - 1, k - 1) + A(n - 1, k))
0

%I #4 Jan 14 2020 14:11:09

%S 1,1,1,1,8,1,1,36,81,1,1,148,1053,1312,1,1,596,10809,37840,32825,1,1,

%T 2388,102645,778384,1766625,1181736,1,1,9556,945297,14096464,63625225,

%U 106140996,57905113,1,1,38228,8593677,240668176,1943042225,6111583956

%N A recursive triangle sequence: A(n,k)=k^2*(A(n - 1, k - 1) + A(n - 1, k))

%C Row sums are:

%C {1, 2, 10, 119, 2515, 82072, 3831780, 242722653, 20048112901, 2093775709630,...}.

%C This sequence resulted from reading the book Combinatorial Identities by _John Riordan_.

%D Review: John Riordan, Combinatorial identities,Paul R. Stein,Bull. Amer. Math. Soc. Volume 78, Number 4 (1972), 490-496.

%F A(n,k)=k^2*(A(n - 1, k - 1) + A(n - 1, k)).

%e {1},

%e {1, 1},

%e {1, 8, 1},

%e {1, 36, 81, 1},

%e {1, 148, 1053, 1312, 1},

%e {1, 596, 10809, 37840, 32825, 1},

%e {1, 2388, 102645, 778384, 1766625, 1181736, 1},

%e {1, 9556, 945297, 14096464, 63625225, 106140996, 57905113, 1},

%e {1, 38228, 8593677, 240668176, 1943042225, 6111583956, 8038259341, 3705927296, 1},

%e {1, 152916, 77687145, 3988189648, 54592760025, 289966542516, 693342321553, 751627944768, 300180111057, 1}

%t A[n_, 1] := 1; A[n_, n_] := 1;

%t A[n_, k_] := k^2*(A[n - 1, k - 1] + A[n - 1, k]);

%t TableForm[Table[A[n, k], {n, 10}, {k, n}], TableAlignments -> Right];

%t Table[Table[A[n, k], {k, n}], {n, 10}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Feb 04 2009