A390477 a(n) = Sum_{k=0..floor(n/6)} (-1)^k * (7*k+1) * binomial(2*n-5*k+1,n-6*k)/(2*n-5*k+1).

1, 1, 2, 5, 14, 42, 131, 421, 1386, 4654, 15886, 54978, 192509, 680899, 2429418, 8734395, 31613985, 115109388, 421354939, 1549721348, 5724315670, 21226681986, 78990800097, 294899059900, 1104220030505, 4145909987441, 15605386349552, 58875964968523

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[(-1)^k*(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, (-1)^k*(7*k+1)*binomial(2*n-5*k+1, n-6*k)/(2*n-5*k+1));
(Magma) [&+[(-1)^k*(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. A059019, A135310, A390476.

Cf. A000108.

Sequence in context: A261588 A006930 A036767 * A261894 A287969 A061922

Adjacent sequences: A390474 A390475 A390476 * A390478 A390479 A390480

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2025

Status

approved