A370456 a(0) = 1, a(n) = (1/2) * Sum_{j=1..n} (1-(-1)^j-(-2)^j) * binomial(n,j) * a(n-j) for n > 0.

1, 2, 6, 29, 192, 1577, 15516, 178229, 2339952, 34559057, 567117876, 10237161629, 201592448712, 4300618438937, 98803485774636, 2432074390036229, 63857242954421472, 1781444969999245217, 52620896463516221796, 1640684857196257578029, 53847865360369426418232

Offset: 0

Author

Prabha Sivaramannair, Feb 23 2024

Keywords

• nonn

Comments

Binomial transform of A370092.

Crossrefs

Cf. A370092, A370163.

Programs

PARI

seq(n)={my(p=exp(x + O(x*x^n))); Vec(serlaplace(2*p^2/(1 + p + p^2 - p^3)))} \\ Andrew Howroyd, Feb 23 2024

SageMath

def a(m):
    if m==0:
        return 1
    else:
        return 1/2*sum([(1-(-2)^j-(-1)^j)*binomial(m,j)*a(m-j) for j in [1,..,m]])
list(a(m) for m in [0,..,20])

Formula

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