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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
OFFSET
1,2
COMMENTS
Also convolution of A045530 with A000984 (central binomial coefficients); also convolution of A045505 with A000302 (powers of 4).
LINKS
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
KEYWORD
easy,nonn
STATUS
approved