A391494 - OEIS

%I #10 Dec 11 2025 10:17:14

%S 1,6,41,286,2006,14090,98967,694752,4873442,34156834,239195387,

%T 1673678190,11701765224,81754091064,570775136884,3982320601808,

%U 27767719611418,193505396179922,1347751048453107,9382179055531386,65281152942526198,454018538186678746

%N Expansion of (g/(2 - g^2))^2, where g = 1+x*g^3 is the g.f. of A001764.

%F G.f.: B(x)^2, where B(x) is the g.f. of A391462.

%F a(n) = (1/(2*n)) * Sum_{k=1..n} k * (k*Pell(k+1) + (k+1)*Pell(k+2)) * binomial(3*n,n-k) for n > 0.

%o (PARI) pell(n) = ([2, 1; 1, 0]^n)[2, 1];

%o a(n) = if(n==0, 1, sum(k=1, n, k*(k*pell(k+1)+(k+1)*pell(k+2))*binomial(3*n, n-k))/(2*n));

%Y Cf. A054146, A391493, A391495.

%Y Cf. A000129, A001764, A391462.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 10 2025