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%I #15 Apr 16 2024 13:34:48
%S 1,2,10,80,838,10952,171910,3148280,65890198,1551389192,40586247910,
%T 1167964662680,36666464437558,1247011549249832,45672691012357510,
%U 1792280373542404280,75021202465129000918,3336499249170658956872,157116438405334017308710,7809681380575733223237080,408621675981135189773468278
%N Binomial transform of A355409.
%F a(0) = 1, a(n) = (-1)^n + Sum_{j=1..n} (1-(-2)^j)*binomial(n,j)*a(n-j) for n > 0.
%F a(0) = 1, a(n) = 1 + Sum_{j=1..n} (3^j-2^j)*binomial(n,j)*a(n-j) for n > 0.
%F E.g.f.: exp(x)/(1 + exp(2*x) - exp(3*x)).
%o (SageMath)
%o def a(n):
%o if n==0:
%o return 1
%o else:
%o return (-1)^n + sum([(1-(-2)^j)*binomial(n,j)*a(n-j) for j in [1,..,n]])
%o list(a(n) for n in [0,..,20])
%o (SageMath)
%o f= e^(x)/(1 + e^(2*x) - e^(3*x))
%o print([(diff(f,x,i)).subs(x=0) for i in [0,..,20]])
%Y Cf. A355409.
%K nonn
%O 0,2
%A _Prabha Sivaramannair_, Mar 24 2024
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