A373388 Alternating row sums of the Eulerian zig-zag number triangle A205497.

1, -1, 1, 0, -1, 0, 5, 0, -45, 0, 665, 0, -14457, 0, 433741, 0, -17160421, 0, 865407905, 0, -54179057649, 0, 4122477869077, 0, -374673778941981, 0, 40087507726395689, 0, -4987405802167886825, 0, 713925031978621041757, 0, -116506260029721326349781, 0, 21501227314690679723073329

Offset

0,7

Links

Table of n, a(n) for n=0..34.

Maple

# Using the recurrence by Kyle Petersen from A205497.
G := proc(n) option remember; local F;
if n = 0 then 1/(1 - q*x) else F := G(n - 1);
simplify((p/(p - q))*(subs({p = q, q = p}, F) - subs(p = q, F))) fi end:
A373388 := n -> subs({p = 1, q = 1, x = -1}, G(n)*(1 - x)^(n + 1)):
seq(A373388(n), n = 0..20);

Mathematica

G[n_] := G[n] = Module[{F}, If[n == 0, 1/(1-q*x), F = G[n-1]; Simplify[ (p/(p-q))*(ReplaceAll[F, {p -> q, q -> p}] - ReplaceAll[F, p -> q])]]]; a[n_] := a[n] = ReplaceAll[G[n]*(1-x)^(n+1), {p -> 1, q -> 1, x -> -1}]; Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Jun 08 2024, after Maple program *)

Crossrefs

Cf. A000111, A205497, A373389.

Sequence in context: A348209 A368768 A297206 * A103709 A122045 A294314

Adjacent sequences: A373385 A373386 A373387 * A373389 A373390 A373391

Keyword

sign

Author

Peter Luschny, Jun 03 2024

Status

approved