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

1,3

Links

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

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

Example

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.

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 *)

Crossrefs

Cf. A006973, A156792.

Sequence in context: A042877 A219517 A232008 * A223532 A041081 A041082

Adjacent sequences: A156788 A156789 A156790 * A156792 A156793 A156794

Keyword

nonn

Author

Gary W. Adamson, Feb 15 2009

Extensions

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

Status

approved