OFFSET
1,6
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
R. J. Mathar, Labeled Trees with fixed node label sum, vixra:1805.0205 (2018).
EXAMPLE
The triangle starts
1;
1 1;
1 1 2;
1 2 3 3;
1 2 6 6 6;
1 3 9 15 16 11;
1 3 13 26 43 37 23;
1 4 17 46 88 116 96 47;
1 4 23 68 169 273 329 239 106;
1 5 28 103 287 585 869 918 622 235;
1 5 35 141 467 1104 2031 2695 2609 1607 551;
1 6 42 195 711 1972 4211 6882 8399 ... 4235 1301;
1 6 50 253 1051 3270 8108 15513 23152 ... ... ;
1 7 58 330 1489 5222 14552 32191 56291 ... ... ;
1 7 68 412 2063 7958 24846 62014 124958 ... ... ;
PROG
(PARI)
EulerMT(u)={my(n=#u, p=x*Ser(u), vars=variables(p)); Vec(exp( sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i ))-1)}
b(n)={my(v=[1]); for(i=1, n, v=concat([1], v + EulerMT(y*v))); Ser(v)*y*(1-x)}
seq(n)={my(g=b(n)); Vec(g + (substvec(g, [x, y], [x^2, y^2]) - g^2)*x/(2*(1-x)) - y)}
{my(A=seq(15)); for(n=1, #A, print(Vecrev(A[n]/y^2)))} \\ Andrew Howroyd, May 20 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, May 01 2018
STATUS
approved