A390481 a(n) = Sum_{k=0..floor(n/6)} (7*k+1) * binomial(2*n-5*k+1,n-6*k)/(2*n-5*k+1).

1, 1, 2, 5, 14, 42, 133, 437, 1474, 5070, 17706, 62594, 223517, 804931, 2919732, 10657195, 39112905, 144243948, 534251361, 1986419632, 7411559420, 27740913054, 104131680951, 391913404280, 1478596569865, 5590875554321, 21184002791280, 80421048491387

Offset

0,3

Links

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

Formula

G.f.: g/(1-x^6*g^7) where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[(7*k+1)*Binomial[2*n-5*k+1, n-6*k]/(2*n-5*k+1), {k, 0, Floor[n/6]}], {n, 0, 30}] (* Vincenzo Librandi, Nov 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\6, (7*k+1)*binomial(2*n-5*k+1, n-6*k)/(2*n-5*k+1));
(Magma) [&+[(7*k+1)*Binomial(2*n-5*k+1, n-6*k)/(2*n-5*k+1): k in [0..Floor(n/6)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A081696, A390478, A390479, A390480.

Cf. A000108, A390477.

Sequence in context: A374548 A393659 A061815 * A340361 A308329 A202061

Adjacent sequences: A390478 A390479 A390480 * A390482 A390483 A390484

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2025

Status

approved