A369746 - OEIS

%I #12 Apr 25 2024 13:22:39

%S 1,3,12,63,423,3528,35559,422901,5817744,91072269,1600588269,

%T 31230827532,670252672593,15696888917427,398454496989012,

%U 10899543418960167,319672849622745951,10007954229075765984,333139545206104991031,11749955670275356579941

%N Expansion of e.g.f. exp( 3 * (1-sqrt(1-2*x)) ).

%F a(0) = 1; a(n) = Sum_{k=0..n-1} 3^(n-k) * (n-1+k)! / (2^k * k! * (n-1-k)!).

%F a(n) = (2*n-3)*a(n-1) + 9*a(n-2).

%p # The row polynomials of A132062 evaluated at x = 3.

%p T := proc(n, k) option remember; if k = 0 then 0^n elif n < k then 0

%p else (2*(n - 1) - k)*T(n - 1, k) + T(n - 1, k - 1) fi end:

%p seq(add(T(n, k)*3^k, k = 0..n), n = 0..19);  # _Peter Luschny_, Apr 25 2024

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*(1-sqrt(1-2*x)))))

%Y Cf. A107104, A144301, A132062.

%Y Cf. A369722.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 30 2024