A075911 Third column of triangle A075500.

1, 30, 625, 11250, 188125, 3018750, 47265625, 728906250, 11133203125, 168996093750, 2554931640625, 38523925781250, 579858642578125, 8717878417968750, 130968170166015625, 1966522521972656250, 29517837677001953125, 442967564392089843750, 6646513462066650390625

Offset

0,2

Comments

The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(5*(m+1)*x)/2!.

Links

Colin Barker, Table of n, a(n) for n = 0..849

Index entries for linear recurrences with constant coefficients, signature (30,-275,750).

Formula

a(n) = A075500(n+3, 3) = (5^n)*S2(n+3, 3) with S2(n, m) = A008277(n, m) (Stirling2).

a(n) = (5^n - 8*10^n + 9*15^n)/2.

G.f.: 1/Product_{k=1..3} (1 - 5*k*x).

E.g.f.: (d^3/dx^3)(((exp(5*x)-1)/5)^3)/3! = (exp(5*x) - 8*exp(10*x) + 9*exp(15*x))/2!.

a(n) = 30*a(n-1) - 275*a(n-2) + 750*a(n-3) for n > 2. - Colin Barker, Dec 11 2015

Mathematica

LinearRecurrence[{30, -275, 750}, {1, 30, 625}, 30] (* Harvey P. Dale, Oct 06 2017 *)

Prog

(PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)) + O(x^30)) \\ Colin Barker, Dec 11 2015

Crossrefs

Cf. A016164, A075912.

Sequence in context: A124099 A028258 A285235 * A001719 A004359 A001777

Adjacent sequences: A075908 A075909 A075910 * A075912 A075913 A075914

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved