A075913 Fifth column of triangle A075500.

1, 75, 3500, 131250, 4344375, 132890625, 3855156250, 107765625000, 2933008203125, 78271552734375, 2058270703125000, 53524929199218750, 1380066321044921875, 35349237725830078125, 900813505310058593750, 22863955398559570312500, 578500758117828369140625

Offset

0,2

Comments

The e.g.f. given below is Sum_{m=0..4}(A075513(5,m)*exp(5*(m+1)*x))/4!.

Links

Colin Barker, Table of n, a(n) for n = 0..714

Index entries for linear recurrences with constant coefficients, signature (75,-2125,28125,-171250,375000).

Formula

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

a(n) = Sum_{m=0..4}(A075513(5, m)*((m+1)*5)^n)/4!.

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

E.g.f.: (d^5/dx^5)((((exp(5*x)-1)/5)^5)/5!) = (exp(5*x) - 64*exp(10*x) + 486*exp(15*x) - 1024*exp(20*x) + 625*exp(25*x))/4!.

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

Mathematica

Table[5^n*(1 - 2^(n+6) + 2*3^(n+5) - 4^(n+5) + 5^(n+4))/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)) + O(x^30)) \\ Colin Barker, Dec 12 2015

Crossrefs

Cf. A000351, A016164, A075911, A075912, A075914.

Sequence in context: A017791 A017738 A166725 * A134228 A324452 A110902

Adjacent sequences: A075910 A075911 A075912 * A075914 A075915 A075916

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved