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A145138 Main diagonal of square array A145153.

%I A145138 #22 May 10 2022 05:24:26
%S A145138 0,1,2,6,20,71,259,960,3597,13586,51635,197223,756380,2910707,
%T A145138 11233311,43460144,168502849,654547456,2546819347,9924285801,
%U A145138 38723794820,151278566731,591628491483,2316065644414,9074988880769,35587925333525,139666503235814,548516611541343
%N A145138 Main diagonal of square array A145153.
%H A145138 Alois P. Heinz, <a href="/A145138/b145138.txt">Table of n, a(n) for n = 0..1000</a>
%F A145138 a(n) = [x^n] x/((1-x-x^4)*(1-x)^(n-1)).
%p A145138 a:= n-> coeftayl(x/(1-x-x^4)/(1-x)^(n-1), x=0, n):
%p A145138 seq(a(n), n=0..30);
%p A145138 # second Maple program:
%p A145138 a:= proc(n) option remember; `if`(n<5, n*(n+1)*(n^2-4*n+6)/6,
%p A145138        a(n-4)+(2*(35*n^3-207*n^2+310*n-78)*a(n-1)-(203*n^3
%p A145138        -1244*n^2+1891*n-130)*a(n-2)+(2*n-7)*(7*n-19)*n*
%p A145138        (10*a(n-3)-2*a(n-5)))/((7*n-26)*(n-1)^2))
%p A145138     end:
%p A145138 seq(a(n), n=0..30);  # _Alois P. Heinz_, Aug 18 2019
%t A145138 a[n_] := SeriesCoefficient[x/(1-x-x^4)/(1-x)^(n-1), {x, 0, n}];
%t A145138 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 10 2022 *)
%Y A145138 Cf. A145153, A000004, A000012, A001477, A000217, A000292, A145126, A145127, A145128, A145129, A145130, A017898, A003269, A098578, A145131, A145132, A145133, A145134, A145135, A145136, A145137.
%K A145138 nonn
%O A145138 0,3
%A A145138 _Alois P. Heinz_, Oct 03 2008