A045505 Convolution of A000108 (Catalan numbers) with A040075.

1, 21, 262, 2525, 20754, 152946, 1040556, 6659037, 40599130, 237978598, 1350216660, 7453221490, 40188242420, 212349718980, 1102352779992, 5634083759325, 28400234400810, 141402315307550, 696257439473860

Offset

0,2

Comments

Also convolution of A045492 with A000984 (central binomial coefficients); also convolution of A042985 with A000302 (powers of 4).

Links

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

Formula

a(n) = binomial(n+5, 4)*(4^(n+1) - A000984(n+5)/A000984(4))/2, A000984(n) = binomial(2*n, n).

G.f. c(x)/(1-4*x)^5, where c(x) = g.f. for Catalan numbers.

Maple

seq(coeff(series((1-sqrt(1-4*x))/(2*x*(1-4*x)^5), x, n+1), x, n), n = 0..20); # G. C. Greubel, Jan 13 2020

Mathematica

Table[Binomial[n+5, 4]*(2^(2*n+1) -Binomial[2*n+10, n+5]/140), {n, 0, 20}] (* G. C. Greubel, Jan 13 2020 *)

Prog

(PARI) vector(21, n, binomial(n+5, 4)*(2^(2*n+1) -binomial(2*n+10, n+5)/140)) \\ G. C. Greubel, Jan 13 2020
(Magma) [Binomial(n+5, 4)*(2^(2*n+1) - Binomial(2*n+10, n+5)/140): n in [0..20]]; // G. C. Greubel, Jan 13 2020
(Sage) [binomial(n+5, 4)*(2^(2*n+1) - binomial(2*n+10, n+5)/140) for n in (0..20)] # G. C. Greubel, Jan 13 2020
(GAP) List([0..20], n-> Binomial(n+5, 4)*(2^(2*n+1) - Binomial(2*n+10, n+5)/140)); # G. C. Greubel, Jan 13 2020

Crossrefs

Sequence in context: A125433 A135122 A231380 * A169895 A092794 A133717

Adjacent sequences: A045502 A045503 A045504 * A045506 A045507 A045508

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved