A035378 Coefficients in expansion of Sum_{k>=0} Product_{j=1..k} (1-x^j) about x = -1.

3, 11, 72, 635, 7085, 95911, 1528541, 28044762, 582314535, 13500314080, 345696545788, 9690223054222, 295132850278639, 9705001713289680, 342693270841135600, 12932930349605422101, 519485442041267214922

Offset: 0

Author

Bill Gosper, Aug 19 2001

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250
• Hsien-Kuei Hwang, and Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], p. 35, 2019.

Crossrefs

Cf. A022493.

Programs

PARI

a(n)=polcoeff(sum(i=0,2*n+1,prod(j=1,i,1-(x-1)^j,1+x*O(x^n))),n)

Formula

a(n) ~ sqrt(12) * exp(Pi^2/48) * 24^(n+1) * n^(n+1) / (exp(n) * Pi^(2*n+2)). - Vaclav Kotesovec, May 04 2014

Conjectures: a(5*n+3) == 0 (mod 5), a(5*n+4) == 0 (mod 5) and a(5*n+2) - 2*a(5*n+1) == (0 mod 5) (all checked up to n = 49). - Peter Bala, Jun 19 2023

Extensions

More terms from Vladeta Jovovic, Aug 20 2001