A370456 - OEIS

%I #31 Feb 28 2024 20:40:10

%S 1,2,6,29,192,1577,15516,178229,2339952,34559057,567117876,

%T 10237161629,201592448712,4300618438937,98803485774636,

%U 2432074390036229,63857242954421472,1781444969999245217,52620896463516221796,1640684857196257578029,53847865360369426418232

%N 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.

%C Binomial transform of A370092.

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

%o (SageMath)

%o def a(m):

%o     if m==0:

%o         return 1

%o     else:

%o         return 1/2*sum([(1-(-2)^j-(-1)^j)*binomial(m,j)*a(m-j) for j in [1,..,m]])

%o list(a(m) for m in [0,..,20])

%o (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

%Y Cf. A370092, A370163.

%K nonn

%O 0,2

%A _Prabha Sivaramannair_, Feb 23 2024