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A290994 p-INVERT of (1,1,1,1,1,...), where p(S) = 1 - S^7. 2
0, 0, 0, 0, 0, 0, 1, 7, 28, 84, 210, 462, 924, 1717, 3017, 5110, 8568, 14756, 27132, 54264, 116281, 257775, 572264, 1246784, 2641366, 5430530, 10861060, 21242341, 40927033, 78354346, 150402700, 291693136, 574274008, 1148548016, 2326683921, 4749439975 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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 A291000 for a guide to related sequences.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 2)

FORMULA

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + 2*a(n-7) for n >= 8.

G.f.: x^6 / ((1 - 2*x)*(1 - 5*x + 11*x^2 - 13*x^3 + 9*x^4 - 3*x^5 + x^6)). - Colin Barker, Aug 22 2017

MATHEMATICA

z = 60; s = x/(1 - x); p = 1 - s^7;

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000012 *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A290994 *)

PROG

(PARI) concat(vector(6), Vec(x^6 / ((1 - 2*x)*(1 - 5*x + 11*x^2 - 13*x^3 + 9*x^4 - 3*x^5 + x^6)) + O(x^50))) \\ Colin Barker, Aug 22 2017

CROSSREFS

Cf. A000012, A289780, A291000.

Sequence in context: A023032 A278969 A000579 * A049017 A019501 A229887

Adjacent sequences:  A290991 A290992 A290993 * A290995 A290996 A290997

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 22 2017

STATUS

approved

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Last modified October 22 20:57 EDT 2018. Contains 316502 sequences. (Running on oeis4.)