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A013615 Triangle of coefficients in expansion of (1+8x)^n. 2
1, 1, 8, 1, 16, 64, 1, 24, 192, 512, 1, 32, 384, 2048, 4096, 1, 40, 640, 5120, 20480, 32768, 1, 48, 960, 10240, 61440, 196608, 262144, 1, 56, 1344, 17920, 143360, 688128, 1835008, 2097152, 1, 64, 1792, 28672, 286720, 1835008, 7340032, 16777216, 16777216 (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,...,8} 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+8y)].

T(n,k) = 8^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*7^(n-i). Row sums are 9^n = A001019. - Mircea Merca, Apr 28 2012

MAPLE

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+8*x)^n):

seq(T(n), n=0..10);  # Alois P. Heinz, Jul 25 2015

CROSSREFS

Sequence in context: A040071 A317026 A126000 * A209242 A103884 A103883

Adjacent sequences:  A013612 A013613 A013614 * A013616 A013617 A013618

KEYWORD

tabl,nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 16 03:51 EST 2019. Contains 319184 sequences. (Running on oeis4.)