A134138 Alternating row sums of triangle A046089 (S1p(3)).

1, 2, 4, 2, -74, -916, -8672, -73564, -542852, -2595016, 18348496, 906083672, 21021502984, 406255974032, 7157641045696, 116383645516784, 1681549859135248, 18311613681506336, -3332917116147392

Offset: 1

Author

Wolfdieter Lang Oct 12 2007

Keywords

• sign
• easy

Crossrefs

Cf. A049377 (row sums of A046089).

Programs

Mathematica

Rest[CoefficientList[Series[1-E^(-x*(2-x)/(2*(1-x)^2)), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 09 2013 *)

Formula

a(n) = Sum_{m=1..n} A046089(n,m)*(-1)^(m-1), n >= 1.

E.g.f.: 1 - exp(-x*(2-x)/(2*(1-x)^2)). Cf. e.g.f. first column of A046089.

a(n) = (3*n-4)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 09 2013

Lim sup n->infinity |a(n)|/(2*n^(n-1/6)*exp(-n^(1/3)/4+3*n^(2/3)/4-n+1/3)/sqrt(3)) = 1. - Vaclav Kotesovec, Oct 09 2013