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A004704
Expansion of e.g.f. 1/(7- Sum_{k=1..6} exp(k*x)).
4
1, 21, 973, 67473, 6238309, 720964881, 99986786773, 16177741934193, 2991473373828709, 622307309978695761, 143840821212045590773, 36572284571798550251313, 10144031468802588684994309, 3048113900510603294243693841
OFFSET
0,2
LINKS
FORMULA
Equals expansion of e.g.f. 1/(7-exp(x)-exp(2*x)-exp(3*x)-exp(4*x)-exp(5*x)-exp(6*x)).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + ... + 6^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020
MATHEMATICA
With[{nn=20}, CoefficientList[Series[1/(7-Exp[x]-Exp[2*x]-Exp[3*x]-Exp[4*x]-Exp[5*x]-Exp[6*x]), {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Jun 14 2012 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(1/(7-sum(k=1, 6, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(7-Exp(x)-Exp(2*x)-Exp(3*x)-Exp(4*x)-Exp(5*x)-Exp(6*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018
CROSSREFS
Column k=6 of A320253.
Sequence in context: A006301 A220384 A184133 * A138473 A273281 A186392
KEYWORD
nonn
STATUS
approved