A378065 a(n) = (-10)^n * Euler(n, 2/5). Row 5 of A378066.

1, 1, -24, -74, 2976, 15376, -906624, -6563024, 514546176, 4789470976, -469222938624, -5338232282624, 627559296638976, 8437702651826176, -1157248322241921024, -17953287144063002624, 2814090582404042981376, 49478116534660975230976, -8724885890905288434253824

Offset: 0

Author

Peter Luschny, Nov 17 2024

Keywords

• sign

Crossrefs

Cf. A378066.

Programs

Maple

a := n -> (-10)^n * euler(n, 2/5): seq(a(n), n = 0..18);
# Or:
ser := series(exp(x)/cosh(5*x), x, 20):
seq(n!*coeff(ser, x, n), n = 0..18);

Formula

a(n) = n! * [x^n] exp(x)/cosh(5*x).

a(n) = Sum_{j=0..n} (-5)^j*binomial(n, j)*Euler(j).