A042941 Convolution of Catalan numbers A000108 with A038845.

1, 13, 110, 765, 4746, 27314, 149052, 781725, 3975730, 19730150, 95973956, 459145778, 2165937060, 10095323460, 46566906872, 212857023069, 965208806082, 4345780250270, 19442667426420, 86489687956518

Offset

0,2

Comments

Also convolution of A018218(n+1), n >= 0, with A000302 (powers of 4); also convolution of A000346 with A002697.

Links

Fung Lam, Table of n, a(n) for n = 0..1000

Formula

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

G.f.: c(x)/(1-4*x)^3, where c(x) is the g.f. for Catalan numbers.

Recurrence: (n+1)*a(n) = 128*(1-2*n)*a(n-4) + 32*(8*n-1)*a(n-3) - 24*(4*n+1)*a(n-2) + 2*(8*n+5)*a(n-1). - Fung Lam, Apr 13 2014

a(n) ~ 2^(2*n)*(n^2 - 8*n^(3/2)/(3*sqrt(Pi))). - Fung Lam, Apr 13 2014

Recurrence: n*(n+1)*a(n) = 2*n*(4*n+9)*a(n-1) - 8*(n+2)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Apr 16 2014

Mathematica

CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x*(1-4*x)^3), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 16 2014 *)

Crossrefs

Sequence in context: A163845 A075143 A005769 * A021344 A119744 A295204

Adjacent sequences: A042938 A042939 A042940 * A042942 A042943 A042944

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved