A045492 Convolution of A000108 (Catalan numbers) with A020920.

1, 19, 218, 1955, 15086, 105102, 679764, 4154403, 24281510, 136887322, 749032492, 3997228430, 20880823820, 107088473660, 540472210728, 2689562860323, 13217998697430, 64240718824930, 309108505173820

Offset

0,2

Comments

Also convolution of A042985 with A000984 (central binomial coefficients); also convolution of A045724 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)*(A000984(n+5)/A000984(4) - 4^(n+2)/(n+5))/2, A000984(n)=binomial(2*n, n);

G.f.: c(x)/(1-4*x)^(9/2) = (2-c(x))/(1-4*x)^5, where c(x) = g.f. for Catalan numbers.

Maple

seq(coeff(series((sqrt(1-4*x) +4*x-1)/(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]*(Binomial[2*n+10, n+5]/140 - 2^(2*n+3)/(n+5)), {n, 0, 20}] (* G. C. Greubel, Jan 13 2020 *)

Prog

(PARI) vector(20, n, binomial(n+4, 4)*(binomial(2*n+8, n+4)/140 - 2^(2*n+1)/(n+4)) ) \\ G. C. Greubel, Jan 13 2020
(Magma) [Binomial(n+5, 4)*(Binomial(2*n+10, n+5)/140 - 2^(2*n+3)/(n+5)): n in [0..20]]; // G. C. Greubel, Jan 13 2020
(Sage) [binomial(n+5, 4)*(binomial(2*n+10, n+5)/140 - 2^(2*n+3)/(n+5)) for n in (0..20)] # G. C. Greubel, Jan 13 2020
(GAP) List([0..20], n-> Binomial(n+5, 4)*(Binomial(2*n+10, n+5)/140 - 2^(2*n+3)/(n+5))); # G. C. Greubel, Jan 13 2020

Crossrefs

Sequence in context: A220978 A367980 A009474 * A026892 A142487 A022743

Adjacent sequences: A045489 A045490 A045491 * A045493 A045494 A045495

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved