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

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A016164, A075912.

Programs

Mathematica

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

PARI

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

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