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A045530 Convolution of A000108 (Catalan numbers) with A020922. 4
1, 23, 310, 3195, 27866, 216566, 1546028, 10338515, 65635570, 399429602, 2346750900, 13384232030, 74417751940, 404759481420, 2159510136408, 11327603405955, 58528412321250, 298354368109930, 1502525977613540 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also convolution of A045505 with A000984 (central binomial coefficients); also convolution of A045492 with A000302 (powers of 4).

LINKS

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

FORMULA

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

G.f. c(x)/(1-4*x)^(11/2), where c(x) = g.f. for Catalan numbers.

MAPLE

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

MATHEMATICA

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

PROG

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

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

(Sage)

def A045530_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

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

A045530_list(40) # G. C. Greubel, Jan 13 2020

CROSSREFS

Sequence in context: A077504 A086558 A090927 * A080188 A142433 A234234

Adjacent sequences:  A045527 A045528 A045529 * A045531 A045532 A045533

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)