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A053113 Expansion of (-1 + 1/(1-10*x)^10)/(100*x); related to A053109. 4
1, 55, 2200, 71500, 2002000, 50050000, 1144000000, 24310000000, 486200000000, 9237800000000, 167960000000000, 2939300000000000, 49742000000000000, 817190000000000000, 13075040000000000000, 204297500000000000000 (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-1)*binomial(n+k,k-1) starting with A000012 (powers of 1), A001792, A036068, A036070, A036083, A036224, A053110-113 for k=1..10.
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Index entries for linear recurrences with constant coefficients, signature (100, -4500, 120000, -2100000, 25200000, -210000000, 1200000000, -4500000000, 10000000000, -10000000000).
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified June 13 03:56 EDT 2024. Contains 373366 sequences. (Running on oeis4.)