A354655 - OEIS

%I #7 Jun 04 2022 08:01:17

%S 3,27,147,630,2295,7476,22302,62100,163260,409080,983367,2280306,

%T 5122026,11184075,23806575,49521456,100872135,201558231,395675475,

%U 764130780,1453424259,2725614243,5044092372,9219499800,16655554125,29759775435,52623867051

%N Column 2 of triangle A354650: a(n) = A354650(n,2), for n >= 1.

%H Paul D. Hanna, <a href="/A354655/b354655.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = (-1)^(n+1) * A354649(n,2), for n >= 1.

%F a(n) = A354650(n,2), for n >= 1.

%o (PARI) {A354650(n,k) = my(A=[1+y]); for(i=1,n, A = concat(A,0);

%o A[#A] = polcoeff(y + sum(m=0,sqrtint(2*#A+9), (-1)^m * x^(m*(m-1)/2) * (1 - x^(2*m+1)) * Ser(A)^(m*(m+1)/2) ),#A-1) );

%o polcoeff(A[n+1],k,y)}

%o for(n=1,30,print1(A354650(n,2),", "))

%Y Cf. A354649, A354650, A354656.

%K nonn

%O 1,1

%A _Paul D. Hanna_, Jun 02 2022