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A045505 Convolution of A000108 (Catalan numbers) with A040075. 4
1, 21, 262, 2525, 20754, 152946, 1040556, 6659037, 40599130, 237978598, 1350216660, 7453221490, 40188242420, 212349718980, 1102352779992, 5634083759325, 28400234400810, 141402315307550, 696257439473860 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 17:43 EDT 2020. Contains 336278 sequences. (Running on oeis4.)