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!)
 A318147 Coefficients of the Omega polynomials of order 3, triangle T(n,k) read by rows with 0<=k<=n. 2
 1, 0, 1, 0, -9, 10, 0, 477, -756, 280, 0, -74601, 142362, -83160, 15400, 0, 25740261, -55429920, 40900860, -12612600, 1401400, 0, -16591655817, 38999319642, -33465991104, 13440707280, -2572970400, 190590400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The name 'Omega polynomial' is not a standard name. LINKS FORMULA Omega(m, n, z) = (m*n)!*[z^(n*m)] H(m, z)^x where H(m, z) = hypergeom([], [seq(i/m, i=1..m-1)], (z/m)^m). We consider here the case m = 3 (for other cases see the cross-references). EXAMPLE [0] [1] [1] [0,            1] [2] [0,           -9,          10] [3] [0,          477,        -756,          280] [4] [0,       -74601,      142362,       -83160,       15400] [5] [0,     25740261,   -55429920,     40900860,   -12612600,     1401400] [6] [0, -16591655817, 38999319642, -33465991104, 13440707280, -2572970400,190590400] MAPLE # See A318146 for the missing functions. FL([seq(CL(OmegaPolynomial(3, n)), n=0..8)]); MATHEMATICA (* OmegaPolynomials are defined in A318146 *) Table[CoefficientList[OmegaPolynomial[3, n], x], {n, 0, 6}] // Flatten PROG (Sage) # See A318146 for the function OmegaPolynomial. [list(OmegaPolynomial(3, n)) for n in (0..6)] CROSSREFS All row sums are 1, alternating row sums (taken absolute) are A002115. T(n,1) ~ A293951(n), T(n,n) = A025035(n). A023531 (m=1), A318146 (m=2), this seq (m=3), A318148 (m=4). Sequence in context: A058200 A067450 A220450 * A324663 A109409 A262551 Adjacent sequences:  A318144 A318145 A318146 * A318148 A318149 A318150 KEYWORD sign,tabl AUTHOR Peter Luschny, Aug 22 2018 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 August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)