OFFSET
0,3
LINKS
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jan 20 2017
EXTENSIONS
More terms from Michel Marcus, Jan 21 2017
STATUS
approved