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A075912 Fourth column of triangle A075500. 5
1, 50, 1625, 43750, 1063125, 24281250, 532890625, 11386718750, 238867578125, 4946347656250, 101481884765625, 2068161621093750, 41943091064453125, 847579699707031250, 17082562164306640625, 343617765808105468750, 6901873153839111328125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The e.g.f. given below is (Sum_{m=0..3} A075513(4,m)*exp(5*(m+1)*x))/3!.

LINKS

Colin Barker, Table of n, a(n) for n = 0..767

Index entries for linear recurrences with constant coefficients, signature (50,-875,6250,-15000).

FORMULA

a(n) = A075500(n+4, 4) = (5^n)*S2(n+4, 4) with S2(n, m) = A008277(n, m) (Stirling2).

a(n) = (Sum_{m=0..3}A075513(4, m)*((m+1)*5)^n, m=0..3)/3!.

G.f.: 1/Product_{k=1..4}(1-5*k*x).

E.g.f.: (d^4/dx^4)((((exp(5*x)-1)/5)^4)/4!) = (-exp(5*x) + 24*exp(10*x) - 81*exp(15*x) + 64*exp(20*x))/3!.

a(n) = 50*a(n-1) - 875*a(n-2) + 6250*a(n-3) - 15000*a(n-4) for n>3. - Colin Barker, Dec 11 2015

MATHEMATICA

Table[5^n*(-1 + 3*2^(3+n) + 2^(6+2*n) - 3^(4+n))/6, {n, 0, 20}] (* Vaclav Kotesovec, Dec 12 2015 *)

PROG

(PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)) + O(x^30)) \\ Colin Barker, Dec 11 2015

CROSSREFS

Cf. A075911, A075913.

Sequence in context: A159183 A159184 A159187 * A062151 A001241 A164986

Adjacent sequences:  A075909 A075910 A075911 * A075913 A075914 A075915

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)