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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
1, 3, 3, 9, 24, 9, 27, 141, 141, 27, 81, 726, 1410, 726, 81, 243, 3471, 11406, 11406, 3471, 243, 729, 15828, 81327, 136872, 81327, 15828, 729, 2187, 69873, 533259, 1390521, 1390521, 533259, 69873, 2187, 6561, 301362, 3295152, 12609198, 19467294, 12609198, 3295152, 301362, 6561, 19683, 1277619, 19489380, 105311556, 237144642, 237144642, 105311556, 19489380, 1277619, 19683 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..54.

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) = x + 3.

EXAMPLE

1

3 3

9 24 9

27 141 141 27

81 726 1410 726 81

243 3471 11406 11406 3471 243

729 15828 81327 136872 81327 15828 729

2187 69873 533259 1390521 1390521 533259 69873 2187

6561 301362 3295152 12609198 19467294 12609198 3295152 301362 6561

PROG

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

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

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); }

tabl(nn) = {for (n=0, nn, for (k=0, n, print1(T(n, k), ", "); ); print(); ); } \\ Michel Marcus, Apr 23 2015

CROSSREFS

Cf. A008292, A256890, A257606, A257607

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

Similar sequences listed in A256890.

Sequence in context: A007683 A316220 A059728 * A184694 A215885 A176158

Adjacent sequences:  A257177 A257178 A257179 * A257181 A257182 A257183

KEYWORD

nonn,tabl

AUTHOR

Dale Gerdemann, Apr 17 2015

STATUS

approved

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Last modified March 29 20:13 EDT 2020. Contains 333117 sequences. (Running on oeis4.)