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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 (list; table; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=0..44.

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: A317054 A292690 A036188 * A243002 A050999 A223450

Adjacent sequences:  A013614 A013615 A013616 * A013618 A013619 A013620

KEYWORD

tabl,nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)