A281351 Irregular triangle read by rows: coefficients of polynomials arising in calculation of squares of certain web-coloring matrices.

1, 1, 2, 2, 6, 12, 6, 1, 26, 73, 72, 24, 12, 156, 516, 732, 480, 120, 2, 126, 1206, 4322, 7680, 7320, 3600, 720, 52, 1408, 11352, 42448, 87652, 106800, 76800, 30240, 5040, 11, 992, 17406, 125444, 480731, 1103460, 1601148, 1486800, 859320, 282240, 40320

Offset

0,3

Links

Table of n, a(n) for n=0..45.

Mark Dukes, Chris D White, Web Matrices: Structural Properties and Generating Combinatorial Identities, arXiv:1603.01589 [math.CO], 2016. See Fig. 6 p. 14.

Mark Dukes, Chris D White, Web Matrices: Structural Properties and Generating Combinatorial Identities, Electronic Journal Of Combinatorics, 23(1) (2016), #P1.45 See Fig. 6 p. 17.

Formula

See Theorem 23 in the Dukes link.

Example

Triangle begins:
1,
1,
2,2,
6,12,6,
1,26,73,72,24,
12,156,516,732,480,120,
2,126,1206,4322,7680,7320,3600,720,
...

Mathematica

row[n_] := If[n<2, {1}, Sum[x^m*Sum[(-1)^(m-b-c) Binomial[j, b] Binomial[m-j, c] Binomial[b c, n], {c, 0, m-j}], {m, 2, 2n}, {j, 1, m-1}, {b, 0, j}] // DeleteCases[CoefficientList[#, x], 0]&];
Table[row[n], {n, 0, 8}] // Flatten (* from PARI *)

Prog

(PARI) vL(n) = if (n==0, [1], select(x->x, Vecrev(sum(m=2, 2*n, x^m*sum(j=1, m-1, sum(b=0, j, sum(c=0, m-j, (-1)^(m-b-c)*binomial(j, b)*binomial(m-j, c)*binomial(b*c, n))))))));
tabf(nn) = for (n=0, nn, rown = vL(n); for (k=1, #rown, print1(rown[k], ", ")); print()); \\ Michel Marcus, Jan 21 2017

Crossrefs

Cf. A269722.

Sequence in context: A335311 A192933 A079005 * A351081 A241669 A356546

Adjacent sequences: A281348 A281349 A281350 * A281352 A281353 A281354

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 20 2017

Extensions

More terms from Michel Marcus, Jan 21 2017

Status

approved