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A171890 Octonomial coefficient array. 11
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 1, 3, 6, 10, 15, 21, 28, 36, 42, 46, 48, 48, 46, 42, 36, 28, 21, 15, 10, 6, 3, 1, 1, 4, 10, 20, 35, 56, 84, 120, 161, 204, 246, 284, 315, 336, 344, 336, 315, 284, 246, 204, 161, 120, 84, 56, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Row lengths are 1,8,15,22,... = 1+7n = A016993(n). Row sums are 1,8,64,... = 8^n = A001018(n). M. F. Hasler, Jun 17 2012

LINKS

T. D. Noe, Rows n = 0..25, flattened

FORMULA

Row n has g.f. (1+x+...+x^7)^n.

T(n,k) = sum {i = 0..floor(k/8)} (-1)^i*binomial(n,i)*binomial(n+k-1-8*i,n-1) for n >= 0 and 0 <= k <= 7*n. - Peter Bala, Sep 07 2013

EXAMPLE

Array begins:

[1]

[1, 1, 1, 1, 1, 1, 1, 1]

[1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1]

...

MAPLE

#Define the r-nomial coefficients for r = 1, 2, 3, ...

rnomial := (r, n, k) -> add((-1)^i*binomial(n, i)*binomial(n+k-1-r*i, n-1), i = 0..floor(k/r)):

#Display the 8-nomials as a table

r := 8:  rows := 10:

for n from 0 to rows do

seq(rnomial(r, n, k), k = 0..(r-1)*n)

end do;

# Peter Bala, Sep 07 2013

MATHEMATICA

Flatten[Table[CoefficientList[(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)^n, x], {n, 0, 10}]] (* T. D. Noe, Apr 04 2011 *)

PROG

(PARI) concat(vector(5, k, Vec(sum(j=0, 7, x^j)^k)))  \\ - M. F. Hasler, Jun 17 2012

CROSSREFS

The q-nomial arrays are for q=2..10: A007318 (Pascal), A027907, A008287,A035343, A063260, A063265, A171890, A213652, A213651.

Sequence in context: A063917 A234344 A279319 * A287793 A073795 A017893

Adjacent sequences:  A171887 A171888 A171889 * A171891 A171892 A171893

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Oct 19 2010

STATUS

approved

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Last modified February 24 05:48 EST 2018. Contains 299597 sequences. (Running on oeis4.)