A294439 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = number of normalized 2n-plets associated to trees with k edges.

1, 1, 2, 1, 6, 5, 1, 14, 28, 14, 1, 30, 110, 120, 42, 1, 62, 375, 682, 495, 132, 1, 126, 1190, 3248, 3731, 2002, 429, 1, 254, 3628, 14062, 23020, 18928, 8008, 1430, 1, 510, 10805, 57516, 127029, 144024, 91392, 31824, 4862, 1, 1022, 31740, 227030, 654395, 968544, 828495, 426360, 125970, 16796

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Marc Bauer and Olivier Golinelli, Random incidence matrices: Moments of the spectral density, arXiv:cond-mat/0007127 [cond-mat.stat-mech], 2000-2001; J. Stat. Phys. 103, 301-307 (2001).

Eva-Maria Hainzl and Élie de Panafieu, Tree walks and the spectrum of random graphs, arXiv:2405.08347 [math.CO], 2024. See p. 4.

Example

Triangle begins:
  1;
  1,    2;
  1,    6,     5;
  1,   14,    28,     14;
  1,   30,   110,    120,     42;
  1,   62,   375,    682,    495,    132;
  1,  126,  1190,   3248,   3731,   2002,    429;
  1,  254,  3628,  14062,  23020,  18928,   8008,   1430;
  1,  510, 10805,  57516, 127029, 144024,  91392,  31824,   4862;
  1, 1022, 31740, 227030, 654395, 968544, 828495, 426360, 125970, 16796;
  ...

Crossrefs

Sequence in context: A046817 A193817 A227159 * A008970 A055896 A193723

Adjacent sequences: A294436 A294437 A294438 * A294440 A294441 A294442

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 20 2017

Status

approved