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 A006135 M4650 #27 Jul 08 2025 16:41:43
%S A006135 1,9,72,626,6084,64974,744193,8965323,112088583,1441465015,
%T A006135 18952951005,253712542005,3447133563343,47425573790397,
%U A006135 659506609478472,9256644358552742,130981854694547790,1866712391002772586
%N A006135 T(n+2,2) from table A045912 of characteristic polynomial of negative Pascal matrix.
%D A006135 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006135 Robert Israel, <a href="/A006135/b006135.txt">Table of n, a(n) for n = 0..200</a>
%H A006135 W. F. Lunnon, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-3/lunnon.pdf">The Pascal matrix</a>, Fib. Quart. vol. 15 (1977) pp. 201-204.
%e A006135 1 + 9*x + 72*x^2 + 626*x^3 + 6084*x^4 + 64974*x^5 + 744193*x^6 + 8965323*x^7 + ...
%p A006135 f:= n -> coeff(LinearAlgebra:-CharacteristicPolynomial(Matrix(n+2,n+2,(i,j) -> -binomial(i+j-2,i-1)),lambda),lambda,2):
%p A006135 map(f, [$0..20]); # _Robert Israel_, Jul 09 2018
%o A006135 (PARI) {a(n) = if( n<0, 0, polcoeff( charpoly( matrix( n+2, n+2, i, j, -binomial( i+j-2, i-1))), 2))} /* _Michael Somos_, Jul 10 2002 */
%Y A006135 Cf. A045912, A006134, A006136.
%K A006135 nonn,easy
%O A006135 0,2
%A A006135 _N. J. A. Sloane_
%E A006135 Edited by _Michael Somos_, Jul 19 2002