A156791 INVERTi transform of A006973.

1, 1, 6, 7, 78, 420, 6872, 17253, 326552, 2680988, 33949242, 386091406, 5974089338, 67562271804, 1708769998136, 16983594666421, 329723068729854, 5611760457560028, 121573316570762036, 2099347805249971662, 50720938223339101844, 1008798617234428297708

Offset: 1

Author

Gary W. Adamson, Feb 15 2009

Keywords

• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..440

Crossrefs

Cf. A006973, A156792.

Programs

Mathematica

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]]}])];
S[n_, x_]:= Sum[A006973[j]*x^j, {j, 0, n+2}];
Rest@With[{p = 100}, CoefficientList[Series[S[p,x]/(x + S[p,x]), {x,0,60}], x]] (* G. C. Greubel, Jun 10 2021 *)

Formula

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

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

Extensions

Terms a(11) onward added by G. C. Greubel, Jun 10 2021