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A075914 Sixth column of triangle A075500. 3
1, 105, 6650, 330750, 14266875, 560896875, 20682062500, 728227500000, 24779833203125, 821666548828125, 26708267167968750, 854772944238281250, 27023254648193359375, 846046877171630859375, 26282219820458984375000, 811330550012329101562500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The e.g.f. given below is Sum_{m=0..5}(A075513(6,m)*exp(5*(m+1)*x))/5!.

LINKS

Colin Barker, Table of n, a(n) for n = 0..675

Index entries for linear recurrences with constant coefficients, signature (105,-4375,91875,-1015000,5512500,-11250000).

FORMULA

a(n) = A075500(n+6, 6) = (5^n)*S2(n+6, 6) with S2(n, m) = A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5}(A075513(6, m)*((m+1)*5)^n)/5!.

G.f.: 1/Product_{k=1..6}(1-5*k*x).

E.g.f.: (d^6/dx^6)((((exp(5*x)-1)/5)^6)/6!) = (-exp(5*x) + 160*exp(10*x) - 2430*exp(15*x) + 10240*exp(20*x) - 15625*exp(25*x) + 7776*exp(30*x))/5!.

G.f.: 1 / ((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)). - Colin Barker, Dec 12 2015

MATHEMATICA

Table[5^(n-1) * (-1 + 5*2^(5+n) + 5*2^(11+2*n) - 10*3^(5+n) - 5^(6+n) + 6^(5+n))/24, {n, 0, 20}] (* Vaclav Kotesovec, Dec 12 2015 *)

PROG

(PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)) + O(x^30)) \\ Colin Barker, Dec 12 2015

CROSSREFS

Cf. A000351, A016164, A075911, A075912, A075913, A075915.

Sequence in context: A075350 A165055 A168306 * A075924 A199353 A263888

Adjacent sequences:  A075911 A075912 A075913 * A075915 A075916 A075917

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)