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

1,2

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).

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).

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 *)

Prog

(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
(Magma) R<x>:=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
(Sage)
def A045624_list(prec):
    P.<x> = 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
(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

Crossrefs

Sequence in context: A193699 A001603 A113403 * A125399 A163146 A037550

Adjacent sequences: A045621 A045622 A045623 * A045625 A045626 A045627

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved