This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053494 #31 Jul 09 2025 01:38:11
%S A053494 1,26,348,2698,14751,62781,222190,681460,1865715,4655535,10756921,
%T A053494 23290026,47700173,93104473,174248451,314246511,548380980,929209095,
%U A053494 1533389605,2470568045,3894914166,6019752376,9136114923,13635769173,20039850376,29033765566
%N A053494 Number of symmetric 5 X 5 matrices of nonnegative integers with every row and column adding to n.
%D A053494 R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986; see Prop. 4.6.21, p. 235, G_5(lambda).
%H A053494 Colin Barker, <a href="/A053494/b053494.txt">Table of n, a(n) for n = 0..1000</a>
%H A053494 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H A053494 R. P. Stanley, <a href="https://pdfs.semanticscholar.org/6054/5d22b1c1ec269264a717b18f3e3d8b346f99.pdf">Magic labelings of graphs, symmetric magic squares,...</a>, Duke Math. J. 43 (3) (1976) 511-531, F_5(x) in Section 5.
%H A053494 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4,-20,40,16,-100,44,110,-110,-44,100,-16,-40,20,4,-5,1).
%F A053494 G.f.: (1 + 21*x + 222*x^2 + 1082*x^3 + 3133*x^4 + 5722*x^5 + 7013*x^6 + 5722*x^7 + 3133*x^8 + 1082*x^9 + 222*x^10 + 21*x^11 + x^12) / ((1-x)^11*(1+x)^6).
%F A053494 a(n) = (189*(59981+5555*(-1)^n) + 18*(2345165+65331*(-1)^n)*n + (76615494+689850*(-1)^n)*n^2 + 40*(2138179+6237*(-1)^n)*n^3 + (63277966+47250*(-1)^n)*n^4 + 1260*(25421+3*(-1)^n)*n^5 + 11171664*n^6 + 2644080*n^7 + 405954*n^8 + 36500*n^9 + 1460*n^10) / 12386304. - _Colin Barker_, Jan 14 2017
%t A053494 CoefficientList[Series[(1+21x+222x^2+1082x^3+3133x^4+5722x^5+7013x^6+5722x^7+3133x^8+1082x^9+222x^10+21x^11+x^12)/((1-x)^11(1+x)^6),{x,0,30}],x] (* or *) LinearRecurrence[ {5,-4,-20,40,16,-100,44,110,-110,-44,100,-16,-40,20,4,-5,1},{1,26,348,2698,14751,62781,222190,681460,1865715,4655535,10756921,23290026,47700173,93104473,174248451,314246511,548380980},30] (* _Harvey P. Dale_, Mar 05 2023 *)
%o A053494 (PARI) Vec((1 + 21*x + 222*x^2 + 1082*x^3 + 3133*x^4 + 5722*x^5 + 7013*x^6 + 5722*x^7 + 3133*x^8 + 1082*x^9 + 222*x^10 + 21*x^11 + x^12) / ((1 - x)^11*(1 + x)^6) + O(x^30)) \\ _Colin Barker_, Jan 14 2017
%Y A053494 Cf. A019298, A053493.
%K A053494 nonn,easy
%O A053494 0,2
%A A053494 _N. J. A. Sloane_, Jan 15 2000
%E A053494 Revised definition, Jul 06 2014