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 A257611 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) = 2*x + 3. 11
 1, 3, 3, 9, 30, 9, 27, 213, 213, 27, 81, 1308, 2982, 1308, 81, 243, 7431, 32646, 32646, 7431, 243, 729, 40314, 310263, 587628, 310263, 40314, 729, 2187, 212505, 2695923, 8701545, 8701545, 2695923, 212505, 2187, 6561, 1099704, 22059036, 113360904, 191433990, 113360904, 22059036, 1099704, 6561 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are: 1, 6, 48, 480, 5760, 80640, 1290240, ... (see A051578). LINKS FORMULA 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) = 2*x + 3. EXAMPLE 1 3 3 9 30 9 27 213 213 27 81 1308 2982 1308 81 243 7431 32646 32646 7431 243 729 40314 310263 587628 310263 40314 729 2187 212505 2695923 8701545 8701545 2695923 212505 2187 6561 1099704 22059036 113360904 191433990 113360904 22059036 1099704 6561 PROG (PARI) f(x) = 2*x + 3; T(n, k) = t(n-k, k); t(n, m) = if (!n && !m, 1, if (n < 0 || m < 0, 0, f(m)*t(n-1, m) + f(n)*t(n, m-1))); tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", "); ); print(); ); \\ Michel Marcus, May 06 2015 CROSSREFS Cf. A060187, A257609, A257613, A257615. Cf. A038221, A257180, A257611, A257620, A257621, A257623, A257625, A257627. Similar sequences listed in A256890. Sequence in context: A010098 A029857 A327712 * A268617 A264412 A202889 Adjacent sequences:  A257608 A257609 A257610 * A257612 A257613 A257614 KEYWORD nonn,tabl AUTHOR Dale Gerdemann, May 06 2015 STATUS approved

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Last modified April 9 14:24 EDT 2020. Contains 333355 sequences. (Running on oeis4.)