A378063 a(n) = (-2*n)^n * Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.

1, 1, -3, -26, 1185, 15376, -2749355, -49816976, 22790134017, 533858404096, -498990299504499, -14365294449638912, 23891962452055766497, 816609772823716089856, -2201371244223771530940315, -87139486416935710159898624, 355987789164484245477279893505

Offset: 0

Author

Peter Luschny, Nov 17 2024

Keywords

• sign

Crossrefs

Cf. A378066.

Programs

Maple

a := n -> ifelse(n = 0, 1, (-2*n)^n * euler(n, (n - 1)/(2*n))):
seq(a(n), n = 0..16);

Formula

a(n) = Sum_{j=0..n} binomial(n, j)*Euler(j)*(-n)^j.