OFFSET
0,11
COMMENTS
Calculates the eleventh 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..960
Index entries for linear recurrences with constant coefficients, signature (66, -1925, 32670, -357423, 2637558, -13339535, 45995730, -105258076, 150917976, -120543840, 39916800).
FORMULA
G.f.: -3628800*x^10 / ((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)*(11*x-1)). - Colin Barker, Sep 20 2013
E.g.f.: Sum_{k=1..11} (-1)^(11-k)*binomial(11-1,k-1)*exp(k*x). - Wolfdieter Lang, May 03 2017
MATHEMATICA
Table[10!*StirlingS2[n+1, 11], {n, 0, 20}] (* Vaclav Kotesovec, Dec 16 2014 *)
CoefficientList[Series[-3628800*x^10 / ((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)*(11*x-1)), {x, 0, 20}], x] (* Vaclav Kotesovec, Dec 16 2014 *)
Table[11^n-10*10^n+45*9^n-120*8^n+210*7^n-252*6^n+210*5^n-120*4^n+45*3^n-10*2^n+1, {n, 0, 20}] (* Vaclav Kotesovec, Dec 16 2014 *)
LinearRecurrence[{66, -1925, 32670, -357423, 2637558, -13339535, 45995730, -105258076, 150917976, -120543840, 39916800}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800}, 30] (* Harvey P. Dale, Mar 20 2017 *)
PROG
(PARI) a(n)=11^n-10*10^n+45*9^n-120*8^n+210*7^n-252*6^n+210*5^n-120*4^n+45*3^n-10*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