A042985 Convolution of A000108 (Catalan numbers) with A038846.

1, 17, 178, 1477, 10654, 69930, 428772, 2496813, 13962982, 75582078, 398302268, 2052354850, 10375356460, 51596749300, 252953904072, 1224672639357, 5863899363510, 27801377704310, 130648178243660, 609082400931158

Offset

0,2

Comments

Also convolution of A045724 with A000984 (central binomial coefficients); also convolution of A042941 with A000302 (powers of 4).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = binomial(n+4, 3)*(4^(n+1) - A000984(n+4)/A000984(3))/2, where A000984(n) = binomial(2*n, n).

G.f.: (1 - sqrt(1-4*x))/(2*x*(1-4*x)^4).

D-finite with recurrence: n*(n+1)*a(n) -2*n*(4*n+13)*a(n-1) +8*(n+3)*(2*n+5)*a(n-2)=0. - R. J. Mathar, Jan 28 2020

Mathematica

CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x*(1-4*x)^4), {x, 0, 20}], x] (* G. C. Greubel, Feb 17 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1-sqrt(1-4*x))/(2*x*(1-4*x)^4)) \\ G. C. Greubel, Feb 17 2019
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!( (1-Sqrt(1-4*x))/(2*x*(1-4*x)^4) )); // G. C. Greubel, Feb 17 2019
(Sage) ((1-sqrt(1-4*x))/(2*x*(1-4*x)^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Feb 17 2019

Crossrefs

Sequence in context: A228214 A246058 A121793 * A125405 A342198 A130651

Adjacent sequences: A042982 A042983 A042984 * A042986 A042987 A042988

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved