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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

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) = 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 July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)