A156791 - OEIS

%I #17 Jun 12 2021 23:20:58

%S 1,1,6,7,78,420,6872,17253,326552,2680988,33949242,386091406,

%T 5974089338,67562271804,1708769998136,16983594666421,329723068729854,

%U 5611760457560028,121573316570762036,2099347805249971662,50720938223339101844,1008798617234428297708

%N INVERTi transform of A006973.

%H G. C. Greubel, <a href="/A156791/b156791.txt">Table of n, a(n) for n = 1..440</a>

%F INVERTi transform of (A006973 with offset 1) = (1, 2, 9, 24, 130, 720, ...).

%F Coefficients of ( S(n, x)/(x + S(n, x)) ), where S(n, x) = Sum_{j=0..n+2} A006973(j)*x^j. - _G. C. Greubel_, Jun 10 2021

%e The sequence begins (1, 1, ...); then for all further a(n), write (n-1) terms of A006973 backwards. Take the dot of the latter and the first (n-1) terms of sequence. Subtract from the next term of A006973.

%e Example: a(4) = 7 = (24 - (9, 2, 1) dot (1, 1, 6)) = 24 - 17.

%t A006973[n_]:= A006973[n]= If[n<4, Max[n-1, 0], (n-1)!*(1 + Sum[k*(-A006973[k]/k!)^(n/k), {k, Most[Divisors[n]]}])];

%t S[n_, x_]:= Sum[A006973[j]*x^j, {j, 0, n+2}];

%t Rest@With[{p = 100}, CoefficientList[Series[S[p,x]/(x + S[p,x]), {x,0,60}], x]] (* _G. C. Greubel_, Jun 10 2021 *)

%Y Cf. A006973, A156792.

%K nonn

%O 1,3

%A _Gary W. Adamson_, Feb 15 2009

%E Terms a(11) onward added by _G. C. Greubel_, Jun 10 2021