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A075913 Fifth column of triangle A075500. 4
1, 75, 3500, 131250, 4344375, 132890625, 3855156250, 107765625000, 2933008203125, 78271552734375, 2058270703125000, 53524929199218750, 1380066321044921875, 35349237725830078125, 900813505310058593750, 22863955398559570312500, 578500758117828369140625 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)