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A289924 p-INVERT of (n!), n >= 1 (A000142, shifted), where p(S) = 1 - S - S^2. 2
1, 4, 17, 79, 402, 2253, 14037, 98152, 774973, 6911131, 69225314, 771593257, 9470565513, 126755983488, 1834510979193, 28511931874423, 473179672441090, 8346048191981797, 155838573499885229, 3069991622444141848, 63618933765102190149, 1383222300396890185731 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0)*x + c(1)*x^2 + c(2)*x^3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the "INVERT" transform of s, so that p-INVERT is a generalization of the "INVERT" transform (e.g., A033453).

See A289780 for a guide to related sequences.

LINKS

Table of n, a(n) for n=0..21.

MATHEMATICA

z = 60; s = Sum[k! x^k, {k, 1, z}]; p = 1 - s - s^2;

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000142 shifted *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1]  (* A289924 *)

CROSSREFS

Cf. A000142.

Sequence in context: A193782 A053486 A151249 * A218134 A110307 A206228

Adjacent sequences:  A289921 A289922 A289923 * A289925 A289926 A289927

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 14 2017

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)