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A013613
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Triangle of coefficients in expansion of (1+6x)^n.
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7
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1, 1, 6, 1, 12, 36, 1, 18, 108, 216, 1, 24, 216, 864, 1296, 1, 30, 360, 2160, 6480, 7776, 1, 36, 540, 4320, 19440, 46656, 46656, 1, 42, 756, 7560, 45360, 163296, 326592, 279936, 1, 48, 1008, 12096, 90720, 435456, 1306368, 2239488, 1679616
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OFFSET
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0,3
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COMMENTS
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T(n,k) equals the number of n-length words on {0,1,...,6} having n-k zeros. - Milan Janjic, Jul 24 2015
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LINKS
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FORMULA
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G.f.: 1 / (1 - x(1+6y)).
T(n,k) = 6^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*5^(n-i). Row sums are 7^n = A000420. - Mircea Merca, Apr 28 2012
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EXAMPLE
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Triangle begins:
1;
1, 6;
1, 12, 36;
1, 18, 108, 216;
1, 24, 216, 864, 1296;
...
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PROG
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(Haskell)
import Data.List (inits)
a013613 n k = a013613_tabl !! n !! k
a013613_row n = a013613_tabl !! n
a013613_tabl = zipWith (zipWith (*))
(tail $ inits a000400_list) a007318_tabl
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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