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 A257180 Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = x + 3. 9

%I

%S 1,3,3,9,24,9,27,141,141,27,81,726,1410,726,81,243,3471,11406,11406,

%T 3471,243,729,15828,81327,136872,81327,15828,729,2187,69873,533259,

%U 1390521,1390521,533259,69873,2187,6561,301362,3295152,12609198,19467294,12609198,3295152,301362,6561,19683,1277619,19489380,105311556,237144642,237144642,105311556,19489380,1277619,19683

%N Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = x + 3.

%C Row sums are: 1, 6, 42, 336, 3024, 30240, 332640, 3991680, 51891840, 726485760, 10897286400, ... (see A001725).

%F T(n,k) = t(n-k, k); t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = x + 3.

%e 1

%e 3 3

%e 9 24 9

%e 27 141 141 27

%e 81 726 1410 726 81

%e 243 3471 11406 11406 3471 243

%e 729 15828 81327 136872 81327 15828 729

%e 2187 69873 533259 1390521 1390521 533259 69873 2187

%e 6561 301362 3295152 12609198 19467294 12609198 3295152 301362 6561

%o (PARI) f(x) = x + 3;

%o T(n, k) = t(n-k, k);

%o t(n, m) = {if (!n && !m, return(1)); if (n < 0 || m < 0, return (0)); f(m)*t(n-1,m) + f(n)*t(n,m-1);}

%o tabl(nn) = {for (n=0, nn, for (k=0, n, print1(T(n, k), ", ");); print(););} \\ _Michel Marcus_, Apr 23 2015

%Y Cf. A008292, A256890, A257606, A257607

%Y Cf. A038221, A257611, A257620, A257621, A257623, A257625, A257627

%Y Similar sequences listed in A256890.

%K nonn,tabl

%O 0,2

%A _Dale Gerdemann_, Apr 17 2015

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)