The On-Line Encyclopedia of Integer Sequences (OEIS)

A053113 revision #10

A053113

Expansion of (-1 + 1/(1-10*x)^10)/(100*x); related to A053109.

1, 55, 2200, 71500, 2002000, 50050000, 1144000000, 24310000000, 486200000000, 9237800000000, 167960000000000, 2939300000000000, 49742000000000000, 817190000000000000, 13075040000000000000, 204297500000000000000

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OFFSET

0,2

COMMENTS

This is the tenth member of the k-family of sequences a(k,n) := k^(n-1)*binomial(n+k,k-1) starting with A000012 (powers of 1), A001792, A036068, A036070, A036083, A036224, A053110-113 for k=1..10.

LINKS

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

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

FORMULA

a(n) = 10^(n-1)*binomial(n+10, 9).

G.f.: (-1 + (1-10*x)^(-10))/(x*10^2).

MATHEMATICA

Table[10^(n - 1)*Binomial[n + 10, 9], {n, 0, 30}] (* _G. C. Greubel_, Aug 16 2018 *)

PROG

(PARI) vector(30, n, n--; 10^(n-1)*binomial(n+10, 9)) \\ _G. C. Greubel_, Aug 16 2018

(MAGMA) [10^(n-1)*Binomial(n+10, 9): n in [0..30]]; // _G. C. Greubel_, Aug 16 2018

CROSSREFS

Sequence in context: A217758 A346325 A240687 * A012048 A215860 A020536

Adjacent sequences: A053110 A053111 A053112 * A053114 A053115 A053116

KEYWORD

easy,nonn

AUTHOR

_Wolfdieter Lang_

STATUS

editing