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%I M4650 #21 Jul 09 2018 08:23:32
%S 1,9,72,626,6084,64974,744193,8965323,112088583,1441465015,
%T 18952951005,253712542005,3447133563343,47425573790397,
%U 659506609478472,9256644358552742,130981854694547790,1866712391002772586
%N T(n+2,2) from table A045912 of characteristic polynomial of negative Pascal matrix.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Robert Israel, <a href="/A006135/b006135.txt">Table of n, a(n) for n = 0..200</a>
%H W. F. Lunnon, <a href="http://www.fq.math.ca/Scanned/15-3/lunnon.pdf">The Pascal matrix</a>, Fib. Quart. vol. 15 (1977) pp. 201-204.
%e 1 + 9*x + 72*x^2 + 626*x^3 + 6084*x^4 + 64974*x^5 + 744193*x^6 + 8965323*x^7 + ...
%p f:= n -> coeff(LinearAlgebra:-CharacteristicPolynomial(Matrix(n+2,n+2,(i,j) -> -binomial(i+j-2,i-1)),lambda),lambda,2):
%p map(f, [$0..20]); # _Robert Israel_, Jul 09 2018
%o (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 Cf. A045912, A006134, A006136.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
%E Edited by _Michael Somos_, Jul 19 2002
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