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A013617
Triangle of coefficients in expansion of (1+10x)^n.
2
1, 1, 10, 1, 20, 100, 1, 30, 300, 1000, 1, 40, 600, 4000, 10000, 1, 50, 1000, 10000, 50000, 100000, 1, 60, 1500, 20000, 150000, 600000, 1000000, 1, 70, 2100, 35000, 350000, 2100000, 7000000, 10000000, 1, 80, 2800, 56000, 700000, 5600000, 28000000, 80000000, 100000000
OFFSET
0,3
COMMENTS
T(n,k) equals the number of n-length words on {0,1,...,10} having n-k zeros. - Milan Janjic, Jul 24 2015
FORMULA
G.f.: 1 / (1 - x(1+10y)).
T(n,k) = 10^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*9^(n-i). Row sums are 11^n = A001020. - Mircea Merca, Apr 28 2012
MAPLE
T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+10*x)^n):
seq(T(n), n=0..10); # Alois P. Heinz, Jul 24 2015
CROSSREFS
Sequence in context: A362371 A362551 A036188 * A243002 A050999 A223450
KEYWORD
tabl,nonn,easy
STATUS
approved