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A257613 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 + 4. 6
1, 4, 4, 16, 48, 16, 64, 416, 416, 64, 256, 3136, 6656, 3136, 256, 1024, 21888, 84608, 84608, 21888, 1024, 4096, 145664, 939520, 1692160, 939520, 145664, 4096, 16384, 939520, 9555456, 28195840, 28195840, 9555456, 939520, 16384, 65536, 5932032, 91475968, 415734784, 676700160, 415734784, 91475968, 5932032, 65536 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are: 1, 8, 80, 960, 13440, 215040, ... (see A051580).

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 + 4.

EXAMPLE

1

4 4

16 48 16

64 416 416 64

256 3136 6656 3136 256

1024 21888 84608 84608 21888 1024

4096 145664 939520 1692160 939520 145664 4096

16384 939520 9555456 28195840 28195840 9555456 939520 16384

65536 5932032 91475968 415734784 676700160 415734784 91475968 5932032 65536

PROG

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

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, A257611, A257615.

Cf. A257606, A257622.

Similar sequences listed in A256890.

Sequence in context: A092266 A219398 A222104 * A223202 A298448 A222144

Adjacent sequences:  A257610 A257611 A257612 * A257614 A257615 A257616

KEYWORD

nonn,tabl

AUTHOR

Dale Gerdemann, May 06 2015

STATUS

approved

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Last modified May 7 06:45 EDT 2021. Contains 343636 sequences. (Running on oeis4.)