A075914 Sixth column of triangle A075500.

1, 105, 6650, 330750, 14266875, 560896875, 20682062500, 728227500000, 24779833203125, 821666548828125, 26708267167968750, 854772944238281250, 27023254648193359375, 846046877171630859375, 26282219820458984375000, 811330550012329101562500

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 A359991 A199353

Adjacent sequences: A075911 A075912 A075913 * A075915 A075916 A075917

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved