The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A321197 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A321197

a(n) gives the A-sequence for the Riordan matrix (1/(1 + x^2 - x^3), x/(1 + x^2 - x^3)) from A321196.
(history; published version)

#7 by Joerg Arndt at Wed Nov 14 01:12:25 EST 2018

STATUS

reviewed

approved

#6 by Peter Luschny at Tue Nov 13 14:44:13 EST 2018

STATUS

proposed

reviewed

#5 by Wolfdieter Lang at Sun Nov 11 02:35:01 EST 2018

STATUS

editing

proposed

#4 by Wolfdieter Lang at Sun Nov 11 02:34:54 EST 2018

FORMULA

a(n) = [t^n] (1/f(t)), where f(t) = F^{[-1]}(t)/t, with the compositional inverse F^{[-1]}(t) of F(x) = 1/(1 + x^2 - x^3). The expansion of f is given by (-1)^n*A001005(n), for n >= 0.

#3 by Wolfdieter Lang at Wed Oct 31 03:28:36 EDT 2018

FORMULA

a(n) = [t^n] (1/f(t)), where f(t) = F^{[-1]}(t)/t, with the compositional inverse of F(x) = 1/(1 + x^2 - x^3). The expansion of f is given in by (-1)^(n+1)*A112455A001005(n), for n >= 0.

CROSSREFS

Cf. A112455, A001005, A321196.

Discussion

Wed Nov 07

14:31

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#2 by Wolfdieter Lang at Tue Oct 30 07:11:41 EDT 2018

NAME

allocated a(n) gives the A-sequence for Wolfdieter Langthe Riordan matrix (1/(1 + x^2 - x^3), x/(1 + x^2 - x^3)) from A321196.

DATA

1, 0, -1, 1, -1, 3, -4, 10, -20, 42, -98, 210, -492, 1122, -2607, 6149, -14443, 34463, -82238, 197574, -476918, 1154402, -2807516, 6845016, -16743674, 41067512, -100967539, 248843095, -614546545, 1520779665

OFFSET

0,6

COMMENTS

See the recurrence formula for A321196 from the A- and Z-sequences.

FORMULA

a(n) = [t^n] (1/f(t)), where f(t) = F^{[-1]}(t)/t, with the compositional inverse of F(x) = 1/(1 + x^2 - x^3). The expansion of f is given in (-1)^(n+1)*A112455(n), for n >= 0.

CROSSREFS

Cf. A112455, A321196.

KEYWORD

allocated

sign

AUTHOR

Wolfdieter Lang, Oct 30 2018

STATUS

approved

editing

#1 by Wolfdieter Lang at Tue Oct 30 05:13:36 EDT 2018

NAME

allocated for Wolfdieter Lang

KEYWORD

allocated

STATUS

approved