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A045492 Convolution of A000108 (Catalan numbers) with A020920. 5
1, 19, 218, 1955, 15086, 105102, 679764, 4154403, 24281510, 136887322, 749032492, 3997228430, 20880823820, 107088473660, 540472210728, 2689562860323, 13217998697430, 64240718824930, 309108505173820 (list; graph; refs; listen; history; text; internal format)
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: A115854 A220978 A009474 * A026892 A142487 A022743

Adjacent sequences:  A045489 A045490 A045491 * A045493 A045494 A045495

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified October 28 07:43 EDT 2021. Contains 348321 sequences. (Running on oeis4.)