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A013614
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Triangle of coefficients in expansion of (1+7x)^n.
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4
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1, 1, 7, 1, 14, 49, 1, 21, 147, 343, 1, 28, 294, 1372, 2401, 1, 35, 490, 3430, 12005, 16807, 1, 42, 735, 6860, 36015, 100842, 117649, 1, 49, 1029, 12005, 84035, 352947, 823543, 823543, 1, 56, 1372, 19208, 168070, 941192, 3294172, 6588344, 5764801
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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,...,7} 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+7y)).
T(n,k) = 7^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*6^(n-i). Row sums are 8^n = A001018. - Mircea Merca, Apr 28 2012
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EXAMPLE
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Triangle starts:
1;
1, 7;
1, 14, 49;
1, 21, 147, 343;
1, 28, 294, 1372, 2401;
1, 35, 490, 3430, 12005, 16807;
...
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MAPLE
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T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+7*x)^n):
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MATHEMATICA
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T[n_, k_] := 7^k*Binomial[n, k];
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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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