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A045624 Row sums of convolution triangle A030526. 3
1, 11, 101, 851, 6885, 54723, 432021, 3403859, 26811397, 211225187, 1664405621, 13116776819, 103376383461, 814752361347, 6421443995733, 50610420076691, 398884119723973, 3143787312038051, 24777605586822197, 195283435452156851 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 15 00:52 EDT 2020. Contains 336484 sequences. (Running on oeis4.)