A331998 Triangle of coefficients of quasi-Stirling polynomials.

1, 1, 3, 1, 13, 16, 1, 39, 171, 125, 1, 101, 1091, 2551, 1296, 1, 243, 5498, 28838, 43653, 16807, 1, 561, 24270, 243790, 780585, 850809, 262144, 1, 1263, 98661, 1733035, 10073955, 22278189, 18689527, 4782969, 1, 2797, 379693, 10996369, 106215619, 410994583, 677785807, 457947691, 100000000

Offset

1,3

Links

Table of n, a(n) for n=1..45.

Sergi Elizalde, Descents on quasi-Stirling permutations, arXiv:2002.00985 [math.CO], 2020. See p. 7.

Example

Triangle begins
1;
1, 3;
1, 13, 16;
1, 39, 171, 125;
1, 101, 1091, 2551, 1296;
1, 243, 5498, 28838, 43653, 16807;

Prog

(PARI)
A(t, z) = (1-t)/(1 - t*exp((1-t)*z));
Q(n, t) = (n!/(n+1))*polcoeff(A(t, z)^(n+1), n, z);
row(n) = my(rowx = Vec(Q(n, t))); vector(n, k, rowx[k]);

Crossrefs

Sequence in context: A133171 A133177 A184828 * A053286 A008826 A103440

Adjacent sequences: A331995 A331996 A331997 * A331999 A332000 A332001

Keyword

nonn,tabl

Author

Michel Marcus, Feb 05 2020

Status

approved