A045622 Convolution of A000108 (Catalan numbers) with A045543.

1, 25, 362, 3973, 36646, 299530, 2238676, 15613741, 103054094, 650194974, 3950996556, 23257207714, 133217073276, 745218012084, 4083224828328, 21966983072637, 116268166691358, 606474982072982, 3122157367765788

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

Author

Wolfdieter Lang

Status

approved