The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A171890 Octonomial coefficient array. 12
 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: A331298 A325351 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 21 01:35 EDT 2021. Contains 343143 sequences. (Running on oeis4.)