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A045622 Convolution of A000108 (Catalan numbers) with A045543. 2
1, 25, 362, 3973, 36646, 299530, 2238676, 15613741, 103054094, 650194974, 3950996556, 23257207714, 133217073276, 745218012084, 4083224828328, 21966983072637, 116268166691358, 606474982072982, 3122157367765788 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also convolution of A045530 with A000984 (central binomial coefficients); also convolution of A045505 with A000302 (powers of 4).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = binomial(n+6, 5)*(4^(n+1) - A000984(n+6)/A000984(5))/2, A000984(n) = binomial(2*n, n).

G.f.: x*c(x)/(1-4*x)^6, where c(x) = g.f. for Catalan numbers.

MAPLE

seq(coeff(series((1-sqrt(1-4*x))/(2*(1-4*x)^6), x, n+1), x, n), n = 0..40); # G. C. Greubel, Jan 13 2020

MATHEMATICA

CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x*(1-4*x)^6), {n, 0, 40}], x] (* G. C. Greubel, Jan 13 2020 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((1-sqrt(1-4*x))/(2*(1-4*x)^6)) \\ G. C. Greubel, Jan 13 2020

(MAGMA) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))/(2*(1-4*x)^6) )); // G. C. Greubel, Jan 13 2020

(Sage)

def A045622_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( (1-sqrt(1-4*x))/(2*(1-4*x)^6) ).list()

A045622_list(40) # G. C. Greubel, Jan 13 2020

CROSSREFS

Sequence in context: A261972 A197678 A197536 * A130052 A059255 A227024

Adjacent sequences:  A045619 A045620 A045621 * A045623 A045624 A045625

KEYWORD

easy,nonn,changed

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)