OFFSET
8,1
LINKS
T. D. Noe, Table of n, a(n) for n=8..200
Daniel J. Bernstein and Andreas Hülsing, Decisional second-preimage resistance: When does SPR imply PRE?, (2019).
Erik Vigren and Andreas Dieckmann, A New Result in Form of Finite Triple Sums for a Series from Ramanujan's Notebooks, Symmetry (2022) Vol. 14, No. 6, 1090.
FORMULA
E.g.f.: ((exp(x) - 1 - x)^4)/4!.
G.f.: x^8*(288*x^6 - 1560*x^5 + 3500*x^4 - 4130*x^3 + 2625*x^2 - 840*x + 105) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^2*(1 - 4*x)).
a(n) = (4^n-3^(n-1)(4n+12)+2^(n-1)(12+9n+3n^2)-4n^3-8n-4)/24. - David Wasserman, Jun 06 2007
EXAMPLE
a(8) = 8!/(2!*2!*2!*2!*4!) = 105.
MAPLE
A058844:=n->(4^n-3^(n-1)*(4*n+12)+2^(n-1)*(12+9*n+3*n^2)-4*n^3-8*n-4)/24: seq(A058844(n), n=8..25); # Wesley Ivan Hurt, Oct 28 2014
MATHEMATICA
Table[(4^n - 3^(n - 1) (4 n + 12) + 2^(n - 1) (12 + 9 n + 3 n^2) - 4 n^3 - 8 n - 4)/24, {n, 8, 25}] (* Wesley Ivan Hurt, Oct 28 2014 *)
offset = 8; terms = 21; egf = (Exp[x]-1-x)^4/4!; Drop[CoefficientList[egf + O[x]^(terms+offset), x]*Range[0, terms+offset-1]!, offset] (* Jean-François Alcover, May 07 2017 *)
PROG
(Magma) [(4^n-3^(n-1)*(4*n+12)+2^(n-1)*(12+9*n+3*n^2)-4*n^3-8*n-4)/24 : n in [8..25]]; // Wesley Ivan Hurt, Oct 28 2014
(PARI) a(n)=(4^n - 3^(n-1)*(4*n+12) + 2^(n-1)*(12+9*n+3*n^2) - 4*n^3 - 8*n - 4)/24 \\ Charles R Greathouse IV, Oct 28 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Michael Steyer, Dec 02 2000
EXTENSIONS
More terms from James A. Sellers, Dec 06 2000
STATUS
approved