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A257612 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 + 2. 10
1, 2, 2, 4, 24, 4, 8, 184, 184, 8, 16, 1216, 3680, 1216, 16, 32, 7584, 53824, 53824, 7584, 32, 64, 46208, 674752, 1507072, 674752, 46208, 64, 128, 278912, 7764096, 33244544, 33244544, 7764096, 278912, 128, 256, 1677312, 84892672, 636233728, 1196803584, 636233728, 84892672, 1677312, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are: 1, 4, 32, 384, 6144, 122880, 2949120, 82575360, ... (see A047053).

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 + 2.

EXAMPLE

1

2 2

4 24 4

8 184 184 8

16 1216 3680 1216 16

32 7584 53824 53824 7584 32

64 46208 674752 1507072 674752 46208 64

128 278912 7764096 33244544 33244544 7764096 278912 128

256 1677312 84892672 636233728 1196803584 636233728 84892672 1677312 256

PROG

(PARI) f(x) = 4*x + 2;

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. A142459, A257621.

Cf. A038208, A256890, A257609, A257610, A257614, A257616, A257617, A257618, A257619.

Cf. similar sequences listed in A256890.

Sequence in context: A263439 A270527 A232275 * A009541 A307969 A212672

Adjacent sequences:  A257609 A257610 A257611 * A257613 A257614 A257615

KEYWORD

nonn,tabl

AUTHOR

Dale Gerdemann, May 06 2015

STATUS

approved

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Last modified February 21 19:49 EST 2020. Contains 332110 sequences. (Running on oeis4.)