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A089574 Column 4 of an array closely related to A083480. (Both arrays have shape sequence A083479).

%I A089574 #17 Aug 28 2018 10:14:46
%S A089574 5,32,113,299,664,1309,2366,4002,6423,9878,14663,21125,29666,40747,
%T A089574 54892,72692,94809,121980,155021,194831,242396,298793,365194,442870,
%U A089574 533195,637650,757827,895433,1052294,1230359,1431704,1658536,1913197
%N A089574 Column 4 of an array closely related to A083480. (Both arrays have shape sequence A083479).
%C A089574 The diagonals are finite and sum to A047970.
%C A089574 Values appear to be a transformation of A006468 (rooted planar maps). Also known as well-labeled trees (cf. A000168).
%C A089574 First differences of the conjectured polynomial formula for A006468. [From _R. J. Mathar_, Jun 26 2010]
%H A089574 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A089574 Row sums are powers of 2.
%F A089574 a(n) = A000330(n) + A006011(n+1) + A034263(n-1).
%F A089574 a(n)= +6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6). G.f.: x*(5+2*x-4*x^2+x^3)/(x-1)^6. a(n) = n*(n+1)*(4*n^3+51*n^2+159*n+86)/120. [From _R. J. Mathar_, Jun 26 2010]
%e A089574 The array begins
%e A089574 1
%e A089574 2
%e A089574 4
%e A089574 7 1
%e A089574 11 5
%e A089574 16 14 2
%e A089574 22 30 12
%e A089574 29 55 39 5
%e A089574 37 91 95 32 1
%Y A089574 Cf. A105552, A006468.
%Y A089574 Cf. A006011, A034261.
%Y A089574 Cf. A000124 (column 1), A000330 (column 2), A086602 (column 3), A107600 (column 5), A107601 (column 6), A109125 (column 7), A109126 (column 8), A109820 (column 9), A108538 (column 10), A109821 (column 11), A110553 (column 12), A110624 (column 13).
%K A089574 nonn,easy
%O A089574 1,1
%A A089574 _Alford Arnold_, Dec 29 2003; extended May 04 2005
%E A089574 Extended beyond a(8) by _R. J. Mathar_, Jun 26 2010