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URL: https://oeis.org/A145138

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A145138
Main diagonal of square array A145153.
2
0, 1, 2, 6, 20, 71, 259, 960, 3597, 13586, 51635, 197223, 756380, 2910707, 11233311, 43460144, 168502849, 654547456, 2546819347, 9924285801, 38723794820, 151278566731, 591628491483, 2316065644414, 9074988880769, 35587925333525, 139666503235814, 548516611541343
OFFSET
0,3
LINKS
FORMULA
a(n) = [x^n] x/((1-x-x^4)*(1-x)^(n-1)).
MAPLE
a:= n-> coeftayl(x/(1-x-x^4)/(1-x)^(n-1), x=0, n):
seq(a(n), n=0..30);
# Alternative:
a:= proc(n) option remember; `if`(n<5, n*(n+1)*(n^2-4*n+6)/6,
a(n-4)+(2*(35*n^3-207*n^2+310*n-78)*a(n-1)-(203*n^3
-1244*n^2+1891*n-130)*a(n-2)+(2*n-7)*(7*n-19)*n*
(10*a(n-3)-2*a(n-5)))/((7*n-26)*(n-1)^2))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Aug 18 2019
MATHEMATICA
a[n_] := SeriesCoefficient[x/(1-x-x^4)/(1-x)^(n-1), {x, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 10 2022 *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 03 2008
STATUS
approved