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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.

%I A370456 #31 Feb 28 2024 20:40:10
%S A370456 1,2,6,29,192,1577,15516,178229,2339952,34559057,567117876,
%T A370456 10237161629,201592448712,4300618438937,98803485774636,
%U A370456 2432074390036229,63857242954421472,1781444969999245217,52620896463516221796,1640684857196257578029,53847865360369426418232
%N 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.
%C A370456 Binomial transform of A370092.
%F A370456 E.g.f.: 2*exp(2*x)/(1 + exp(x) + exp(2*x) - exp(3*x)).
%o A370456 (SageMath)
%o A370456 def a(m):
%o A370456     if m==0:
%o A370456         return 1
%o A370456     else:
%o A370456         return 1/2*sum([(1-(-2)^j-(-1)^j)*binomial(m,j)*a(m-j) for j in [1,..,m]])
%o A370456 list(a(m) for m in [0,..,20])
%o A370456 (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 A370456 Cf. A370092, A370163.
%K A370456 nonn
%O A370456 0,2
%A A370456 _Prabha Sivaramannair_, Feb 23 2024