A371460 Binomial transform of A355409.

1, 2, 10, 80, 838, 10952, 171910, 3148280, 65890198, 1551389192, 40586247910, 1167964662680, 36666464437558, 1247011549249832, 45672691012357510, 1792280373542404280, 75021202465129000918, 3336499249170658956872, 157116438405334017308710, 7809681380575733223237080, 408621675981135189773468278

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1, a(n) = (-1)^n + Sum_{j=1..n} (1-(-2)^j)*binomial(n,j)*a(n-j) for n > 0.

a(0) = 1, a(n) = 1 + Sum_{j=1..n} (3^j-2^j)*binomial(n,j)*a(n-j) for n > 0.

E.g.f.: exp(x)/(1 + exp(2*x) - exp(3*x)).

Prog

(SageMath)
def a(n):
    if n==0:
        return 1
    else:
        return (-1)^n + sum([(1-(-2)^j)*binomial(n, j)*a(n-j) for j in [1, .., n]])
list(a(n) for n in [0, .., 20])
(SageMath)
f= e^(x)/(1 + e^(2*x) - e^(3*x))
print([(diff(f, x, i)).subs(x=0) for i in [0, .., 20]])

Crossrefs

Cf. A355409.

Sequence in context: A003578 A274276 A152600 * A220112 A367851 A048286

Adjacent sequences: A371457 A371458 A371459 * A371461 A371462 A371463

Keyword

nonn

Author

Prabha Sivaramannair, Mar 24 2024

Status

approved