A220901 Triangle read by rows: k-th "a-number" of star graph K_{1,n-1}.

1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 4, 8, 1, 5, 20, 16, 1, 6, 40, 96, 1, 7, 70, 336, 272, 1, 8, 112, 896, 2176, 1, 9, 168, 2016, 9792, 7936, 1, 10, 240, 4032, 32640, 79360, 1, 11, 330, 7392, 89760, 436480, 353792, 1, 12, 440, 12672, 215424, 1745920, 4245504

Offset: 0

Author

N. J. A. Sloane, Jan 01 2013

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1;
  1;
  1, 1;
  1, 2;
  1, 3,  2;
  1, 4,  8;
  1, 5, 20,  16;
  1, 6, 40,  96;
  1, 7, 70, 336, 272;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..200, flattened
• Suyoung Choi and Hanchul Park, A new graph invariant arises in toric topology, arXiv preprint arXiv:1210.3776 [math.AT], 2012-2013. See Table 4.

Programs

Mathematica

t[n_, k_] := t[n, k] = If[k == 0, Boole[n == 0], t[n, k-1] + t[n-1, n-k]];
T[n_, k_] := If[k == 0, 1, Binomial[n-1, 2k-1] t[2k-1, 2k-1]];
Table[T[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}] // Flatten (* Jean-François Alcover, Oct 06 2018 *)

PARI

T(n,k) = {if (k == 0, return(1)); binomial(n - 1, 2*k - 1)*(2*k - 1)!*polcoeff(tan(x + O(x^(2*n + 2))), 2*k - 1);} \\ Michel Marcus, Feb 07 2013

Formula

T(n,k) = binomial(n-1, 2*k-1)*A000111(2*k-1) (see Theorem 2.9 in paper). - Michel Marcus, Feb 07 2013

Extensions

More terms from Michel Marcus, Feb 07 2013