A371768 - OEIS

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A371768

a(n) = n! * [x^n] (log(2*x - 1) - log(x - 1) - log(x + 1)) / (x - 1). Row sums of A371685.

0, 2, 6, 34, 220, 1868, 18648, 222696, 3061728, 48199392, 852857280, 16813212480, 365177928960, 8671294183680, 223409173317120, 6207795845798400, 185021865565286400, 5887763630809804800, 199220359130518118400, 7141874528908565913600, 270391380094261923840000

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

MAPLE

assume(x > 0): egf := (log(2*x - 1) - log(x - 1) - log(x + 1))/(x - 1):

ser := series(egf, x, 24): seq(n!*coeff(ser, x, n), n = 0..20);

# Recurrence:

a := proc(n) option remember; if n < 4 then return [0, 2, 6, 34][n+1] fi;

(2*(n-4)^4 + 14*(n-4)^3 + 34*(n-4)^2 + 34*n - 124)*a(n-4) - (3*(n-4)^3 + 19*(n-4)^2 + 38*n - 128)*a(n-3) - ((n-4)^2 + 7*n - 16)*a(n-2) + (3*n - 2)*a(n-1) end:

seq(a(n), n = 0..20);

CROSSREFS

Cf. A371685.

Sequence in context: A018953 A009199 A052824 * A019029 A019032 A108424

Adjacent sequences: A371765 A371766 A371767 * A371769 A371770 A371771

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 09 2024

STATUS

approved