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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 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. 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 Adjacent sequences: A053110 A053111 A053112 * A053114 A053115 A053116 KEYWORD easy,nonn AUTHOR Wolfdieter Lang STATUS approved

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