The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A287698 Square array A(n,k) = (n!)^3 [x^n] hypergeom([], [1, 1], z)^k read by antidiagonals. 7
 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 10, 1, 0, 1, 4, 27, 56, 1, 0, 1, 5, 52, 381, 346, 1, 0, 1, 6, 85, 1192, 6219, 2252, 1, 0, 1, 7, 126, 2705, 36628, 111753, 15184, 1, 0, 1, 8, 175, 5136, 124405, 1297504, 2151549, 104960, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Let A_m(n,k) = (n!)^m [x^n] hypergeom([], [1,…,1], z)^k where [1,…,1] lists (m-1) times 1. These arrays can be seen as generalizations of the power functions n^k. For m = 1 -> A003992, m = 2 -> A287316, m = 3 -> A287698. A_m(n,n) is the sum of m-th powers of coefficients in the full expansion of (z_1+z_2+...+z_n)^n (compare A245397). A287696 provide polynomials and A287697 rational functions generating the columns of the array. LINKS Table of n, a(n) for n=0..54. EXAMPLE Array starts: k\n| 0 1 2 3 4 5 6 7 ---|------------------------------------------------------------------- k=0| 1, 0, 0, 0, 0, 0, 0, 0, ... A000007 k=1| 1, 1, 1, 1, 1, 1, 1, 1, ... A000012 k=2| 1, 2, 10, 56, 346, 2252, 15184, 104960, ... A000172 k=3| 1, 3, 27, 381, 6219, 111753, 2151549, 43497891, ... A141057 k=4| 1, 4, 52, 1192, 36628, 1297504, 50419096, 2099649808, ... A287699 k=5| 1, 5, 85, 2705, 124405, 7120505, 464011825, 33031599725, ... k=6| 1, 6, 126, 5136, 316206, 25461756, 2443835736, 263581282656, ... A001107,A287702,A287700, A287701, A055733 MAPLE A287698_row := (k, len) -> seq(A287696_poly(j)(k), j=0..len): A287698_row := proc(k, len) hypergeom([], [1, 1], x): series(%^k, x, len); seq((i!)^3*coeff(%, x, i), i=0..len-1) end: for k from 0 to 6 do A287698_row(k, 9) od; A287698_col := proc(n, len) local k, x; hypergeom([], [1, 1], z); series(%^x, z=0, n+1): unapply(n!^3*coeff(%, z, n), x); seq(%(j), j=0..len) end: for n from 0 to 7 do A287698_col(n, 9) od; MATHEMATICA Table[Table[SeriesCoefficient[HypergeometricPFQ[{}, {1, 1}, x]^k, {x, 0, n}] (n!)^3, {n, 0, 6}], {k, 0, 9}] (* as a table of rows *) CROSSREFS Rows: A000007 (k=0), A000012 (k=1), A000172 (k=2), A141057 (k=3), A287699 (k=4). Columns: A000172 (n=1), A001477(n=1), A001107 (n=2), A287702 (n=3), A287700 (n=4), A287701 (n=5). Cf. A055733 (diagonal), A287696, A287697, A003992, A287316, A245397. Sequence in context: A305466 A160114 A213028 * A366834 A109970 A116088 Adjacent sequences: A287695 A287696 A287697 * A287699 A287700 A287701 KEYWORD nonn,tabl AUTHOR Peter Luschny, May 30 2017 STATUS approved

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

Last modified September 16 07:48 EDT 2024. Contains 375959 sequences. (Running on oeis4.)