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A053109 Expansion of 1/(1-10*x)^10. 4
1, 100, 5500, 220000, 7150000, 200200000, 5005000000, 114400000000, 2431000000000, 48620000000000, 923780000000000, 16796000000000000, 293930000000000000, 4974200000000000000, 81719000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the tenth member of the k-family of sequences a(k,n) := k^n*binomial(n+k-1,k-1) starting with A000012 (powers of 1), A001787(n+1), A027472(n+3), A038846, A036071, A036084, A036226, A053107-9 for k=1..10.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..400

FORMULA

a(n) = 10^n*binomial(n+9, 9);

G.f.: 1/(1-10*x)^10.

MAPLE

seq(coeff(series(1/(1-10*x)^10, x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Aug 16 2018

MATHEMATICA

CoefficientList[Series[1/(1-10x)^10, {x, 0, 20}], x] (* or *) Table[10^n Binomial[n+9, 9], {n, 0, 20}] (* Harvey P. Dale, May 19 2011 *)

PROG

(Sage)[lucas_number2(n, 10, 0)*binomial(n, 9)/10 ^9 for n in xrange(9, 24)] # Zerinvary Lajos, Mar 13 2009

(PARI) vector(30, n, n--; 10^n*binomial(n+9, 9)) \\ G. C. Greubel, Aug 16 2018

(MAGMA) [10^n*Binomial(n+9, 9): n in [0..30]]; // G. C. Greubel, Aug 16 2018

(GAP) List([0..15], n->10^n*Binomial(n+9, 9)); # Muniru A Asiru, Aug 16 2018

CROSSREFS

Sequence in context: A035810 A017763 A204081 * A151647 A245666 A210814

Adjacent sequences:  A053106 A053107 A053108 * A053110 A053111 A053112

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)