A045624 Row sums of convolution triangle A030526.

1, 11, 101, 851, 6885, 54723, 432021, 3403859, 26811397, 211225187, 1664405621, 13116776819, 103376383461, 814752361347, 6421443995733, 50610420076691, 398884119723973, 3143787312038051, 24777605586822197, 195283435452156851

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
• Index entries for linear recurrences with constant coefficients, signature (17,-102,272,-272).

Programs

GAP

a:=[1,11,101,851];; for n in [5..40] do a[n]:=17*a[n-1]-102*a[n-2] +272*a[n-3]-272*a[n-4]; od; a; # G. C. Greubel, Jan 13 2020

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1-6*x+16*x^2-16*x^3)/(1-17*x+102*x^2-272*x^3 + 272*x^4) )); // G. C. Greubel, Jan 13 2020

Maple

seq(coeff(series(x*(1-6*x+16*x^2-16*x^3)/(1-17*x+102*x^2-272*x^3 + 272*x^4), x, n+1), x, n), n = 1..40); # G. C. Greubel, Jan 13 2020

Mathematica

Rest@CoefficientList[Series[x*(1-6*x+16*x^2-16*x^3)/(1-17*x+102*x^2-272*x^3 + 272*x^4), {x,0,40}], x] (* G. C. Greubel, Jan 13 2020 *)

PARI

my(x='x+O('x^40)); Vec(x*(1-6*x+16*x^2-16*x^3)/(1-17*x+102*x^2-272*x^3 + 272*x^4)) \\ G. C. Greubel, Jan 13 2020

Sage

def A045624_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1-6*x+16*x^2-16*x^3)/(1-17*x+102*x^2-272*x^3 + 272*x^4) ).list()
a=A045624_list(40); a[1:] # G. C. Greubel, Jan 13 2020

Formula

G.f.: x*(1 -6*x +16*x^2 -16*x^3)/(1 -17*x +102*x^2 -272*x^3 +272*x^4) = g1(5, x)/(1-g1(5, x)), g1(5, x) := x*(1-6*x+16*x^2-16*x^3)/(1-4*x)^4 (G.f. first column of A030526).