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A257621 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) = 4*x + 3. 8
1, 3, 3, 9, 42, 9, 27, 393, 393, 27, 81, 3156, 8646, 3156, 81, 243, 23631, 142446, 142446, 23631, 243, 729, 171006, 2015895, 4273380, 2015895, 171006, 729, 2187, 1216725, 26107983, 102402705, 102402705, 26107983, 1216725, 2187, 6561, 8584872, 320039388, 2136524184, 3891302790, 2136524184, 320039388, 8584872, 6561 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are: 1, 6, 60, 840, 15120, 332640, 8648640, 259459200, 8821612800, 335221286400, 14079294028800, ... (see A000407).

LINKS

Table of n, a(n) for n=0..44.

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) = 4*x + 3.

EXAMPLE

1

3 3

9 42 9

27 393 393 27

81 3156 8646 3156 81

243 23631 142446 142446 23631 243

729 171006 2015895 4273380 2015895 171006 729

2187 1216725 26107983 102402705 102402705 26107983 1216725 2187

6561 8584872 320039388 2136524184 3891302790 2136524184 320039388 8584872 6561

CROSSREFS

Cf. A142459, A257612.

Cf. A038221, A257180, A257611, A257620, A257623, A257625, A257627.

Similar sequences listed in A256890.

Sequence in context: A100239 A245023 A038080 * A190960 A257623 A257625

Adjacent sequences:  A257618 A257619 A257620 * A257622 A257623 A257624

KEYWORD

nonn,tabl

AUTHOR

Dale Gerdemann, May 09 2015

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)