A390742 a(n) = Sum_{k=0..n} (-1)^k * (2*k+1) * binomial(5*n-3*k+1,n-k)/(5*n-3*k+1).

1, 0, 3, 21, 178, 1612, 15332, 151054, 1528338, 15787951, 165830186, 1765738401, 19016521496, 206785426797, 2267235266453, 25037068981440, 278222528752403, 3108873365802472, 34909927188661606, 393736176480070241, 4458421455114293140, 50665527460992590759

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..920

Formula

G.f.: g/(1+x*g^2) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(-1)^k*(2*k+1)*Binomial[5*n -3*k+1, n-k]/(5*n-3*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(2*k+1)*binomial(5*n-3*k+1, n-k)/(5*n-3*k+1));
(Magma) [&+[(-1)^k*(2*k+1)*Binomial(5*n-3*k+1, n-k)/(5*n-3*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A390741, A390743, A390744.

Cf. A002294.

Sequence in context: A257675 A372108 A195105 * A285272 A295541 A369941

Adjacent sequences: A390739 A390740 A390741 * A390743 A390744 A390745

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved