A391079 Expansion of g^2/(1 - x^3*g^2), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 9, 53, 344, 2416, 17851, 136695, 1075135, 8633653, 70491448, 583411552, 4883449144, 41270081034, 351647260233, 3017640875389, 26057364802975, 226244678579433, 1973996849367207, 17298633233791709, 152189559585752851, 1343702742406693141

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(4*n-10*k+2,n-3*k)/(2*n-5*k+1).

Mathematica

Table[Sum[ (k+1)*Binomial[4* n-10*k+2, n-3*k]/(2*n-5*k+1), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (k+1)*binomial(4*n-10*k+2, n-3*k)/(2*n-5*k+1));
(Magma) [&+[(k+1)*Binomial(4*n-10*k+2, n-3*k)/(2*n-5*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A389653, A391081, A391083.

Cf. A002293.

Sequence in context: A367390 A080146 A389653 * A391081 A391083 A074602

Adjacent sequences: A391076 A391077 A391078 * A391080 A391081 A391082

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved