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A075911 Third column of triangle A075500. 7
1, 30, 625, 11250, 188125, 3018750, 47265625, 728906250, 11133203125, 168996093750, 2554931640625, 38523925781250, 579858642578125, 8717878417968750, 130968170166015625, 1966522521972656250, 29517837677001953125, 442967564392089843750, 6646513462066650390625 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 10:33 EST 2020. Contains 331193 sequences. (Running on oeis4.)