A390147 Expansion of g^2/(1 - x^2*g^2), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 10, 56, 363, 2540, 18719, 143084, 1123888, 9015938, 73553356, 608356076, 5089508859, 42992095102, 366179399391, 3141310120084, 27117461481521, 235389702516728, 2053329861556631, 17990275294687148, 158246298370021478, 1396954300222929984

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Robert Israel, Linear recurrence of order 16

Formula

a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(4*n-6*k+2,n-2*k)/(2*n-3*k+1).

D-finite with recurrence of order 16 (see link). - Robert Israel, May 20 2026

Mathematica

Table[Sum[ (k+1)*Binomial[4* n-6*k+2, n-2*k]/(2*n-3*k+1), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (k+1)*binomial(4*n-6*k+2, n-2*k)/(2*n-3*k+1));
(Magma) [&+[(k+1)*Binomial(4*n-6*k+2, n-2*k)/(2*n-3*k+1): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A389112, A391080, A391082, A391084.

Cf. A002293.

Sequence in context: A243644 A000172 A097971 * A191277 A290443 A336961

Adjacent sequences: A390144 A390145 A390146 * A390148 A390149 A390150

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved