OFFSET
0,10
COMMENTS
Calculates the tenth column of coefficients with respect to the derivatives, d^n/dx^n(y), of the logistic equation when written as y = 1/[1+exp(-x)].
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).
FORMULA
G.f.: 362880*x^9 / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)). - Colin Barker, Sep 20 2013
E.g.f.: Sum_{k=1..10} (-1)^(10-k)*binomial(10-1,k-1)*exp(k*x). - Wolfdieter Lang, May 03 2017
MATHEMATICA
Table[9!*StirlingS2[n+1, 10], {n, 0, 20}] (* Vaclav Kotesovec, Dec 16 2014 *)
Table[10^n-9*9^n+36*8^n-84*7^n+126*6^n-126*5^n+84*4^n-36*3^n+9*2^n-1, {n, 0, 20}] (* Vaclav Kotesovec, Dec 16 2014 *)
CoefficientList[Series[362880*x^9 / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)), {x, 0, 20}], x] (* Vaclav Kotesovec, Dec 16 2014 after Colin Barker *)
PROG
(PARI) a(n)=10^n-9*9^n+36*8^n-84*7^n+126*6^n-126*5^n+84*4^n-36*3^n+9*2^n-1
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard V. Scholtz, III, Sep 07 2013
EXTENSIONS
Offset corrected by Vaclav Kotesovec, Dec 16 2014
STATUS
approved