A393658 Expansion of (1/x) * Series_Reversion( x * ( Sum_{k=0..5} (-x)^k ) ).

1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1724, 3538, 7276, 16201, 40869, 113221, 321779, 893021, 2372381, 6032555, 14859450, 36152505, 88806120, 223972452, 582510646, 1549277266, 4153622296, 11084405260, 29241378024, 76201652329, 196935452341, 507973181189

Offset

0,7

Links

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

Formula

G.f.: (1/x) * Series_Reversion( x * (1-x^6) / (1+x) ).

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

Mathematica

CoefficientList[Normal@Series[InverseSeries@Series[x*((1-x^6)/(1+x)), {x, 0, 50}]/x, {x, 0, 37}], x] (* Vincenzo Librandi, Mar 26 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\6, binomial(n+k, k)*binomial(n+1, n-6*k))/(n+1);
(Magma) N := 35; R<x> := PowerSeriesRing(Rationals(), N+5); f:= x*((1-x^6)/(1+x)); g:= Reverse(f) div x; Coeffs := [Coefficient(g, i):i in [0..N]]; Coeffs; // Vincenzo Librandi, Mar 26 2026

Crossrefs

Cf. A393659, A393660.

Sequence in context: A373912 A212386 A333883 * A373911 A389445 A373910

Adjacent sequences: A393655 A393656 A393657 * A393659 A393660 A393661

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2026

Status

approved