A390592 a(n) = Sum_{k=0..n} (-1)^k * binomial(4*n-k+4,n-k).

1, 7, 56, 468, 4013, 34998, 308914, 2751280, 24675260, 222540723, 2016212292, 18336279440, 167293939222, 1530536505116, 14035961015318, 128987030592224, 1187541309845996, 10951191069804012, 101136784765554976, 935251739450203948, 8658945977177384989

Offset

0,2

Links

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

Formula

G.f.: g^4/((1-4*x*g^3) * (1+x*g^3)) where g = 1+x*g^4 is the g.f. of A002293.

a(n) = Sum_{k=0..n} (-2)^k * binomial(4*n+5,n-k).

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

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

Mathematica

Table[Sum[(-1)^k*Binomial[4*n-k+4, n-k], {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(4*n-k+4, n-k));
(Magma) [&+[(-1)^k*Binomial(4*n-k+4, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 12 2025

Crossrefs

Cf. A147855, A386821, A390547, A390589.

Cf. A002293.

Sequence in context: A155197 A147839 A126694 * A387009 A305198 A264912

Adjacent sequences: A390589 A390590 A390591 * A390593 A390594 A390595

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2025

Status

approved