A391460 Expansion of g/(2 - g^2)^2, where g = 1+x*g^2 is the g.f. of A000108.

1, 5, 28, 155, 845, 4547, 24208, 127754, 669271, 3484423, 18044572, 93015958, 477544394, 2442987822, 12458091056, 63350285588, 321318018891, 1625983154015, 8210737675300, 41382087212510, 208197617452294, 1045762538121162, 5244911849206784, 26268723644049228

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1451

Formula

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

D-finite with recurrence: (32 + 64*n)*a(n) + (96 + 112*n)*a(n + 1) + (112 + 32*n)*a(n + 2) + (-128 - 32*n)*a(n + 3) + (-78 - 16*n)*a(n + 4) + (50 + 9*n)*a(n + 5) + (-n - 6)*a(n + 6) = 0. - Robert Israel, Feb 12 2026

Maple

f:= gfun:-rectoproc({(32 + 64*n)*a(n) + (96 + 112*n)*a(n + 1) + (112 + 32*n)*a(n + 2) + (-128 - 32*n)*a(n + 3) + (-78 - 16*n)*a(n + 4) + (50 + 9*n)*a(n + 5) + (-n - 6)*a(n + 6), a(0) = 1, a(1) = 5, a(2) = 28, a(3) = 155, a(4) = 845, a(5) = 4547}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Feb 12 2026

Prog

(PARI) pell(n) = ([2, 1; 1, 0]^n)[2, 1];
a(n) = if(n==0, 1, sum(k=1, n, k*(k+1)*pell(k+2)*binomial(2*n, n-k))/(2*n));

Crossrefs

Cf. A391463, A391466.

Cf. A000129.

Sequence in context: A126699 A267828 A164537 * A015536 A271808 A005785

Adjacent sequences: A391457 A391458 A391459 * A391461 A391462 A391463

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved