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%I #9 Feb 25 2019 00:07:10
%S 1,3,15,90,629,5019,45030,448776,4919321,58825415,762089899,
%T 10633219662,158974192987,2535484008225,42970371055268,
%U 771162539117408,14609924404202130,291386317037291622,6102681801481066642,133910606028043519500,3072216586896101950757
%N A diagonal of irregular triangle A201949.
%C G.f. of row n in triangle A201949 equals Product_{k=0..n-1} (1 + k*x + x^2).
%F E.g.f.: Sum_{n>=0} log(1 - x)^(2*n+2) / (n!*(n+2)!). - _Paul D. Hanna_, Feb 25 2019
%F a(n) = [x^(n-2)] Product_{k=0..n-1} (1 + k*x + x^2).
%e E.g.f.: A(x) = x^2/2! + 3*x^3/3! + 15*x^4/4! + 90*x^5/5! + 629*x^6/6! + 5019*x^7/7! + 45030*x^8/8! + 448776*x^9/9! + 4919321*x^10/10! + ...
%e Triangle A201949 begins:
%e [1],
%e [1, 0, 1],
%e [(1), 1, 2, 1, 1],
%e [1,(3), 5, 6, 5, 3, 1],
%e [1, 6, (15), 24, 28, 24, 15, 6, 1],
%e [1, 10, 40, (90), 139, 160, 139, 90, 40, 10, 1],
%e [1, 15, 91, 300, (629), 945, 1078, 945, 629, 300, 91, 15, 1], ...
%e where coefficients in parenthesis form the initial terms of this sequence.
%o (PARI) {a(n) = polcoeff( prod(j=0, n-1, 1 + j*x + x^2), n-2)}
%o for(n=2,30,print1(a(n),", "))
%Y Cf. A201949, A201950, A201951, A201952.
%K nonn
%O 2,2
%A _Paul D. Hanna_, Dec 06 2011
%E Offset changed to 2 to agree with the e.g.f. - _Paul D. Hanna_, Feb 25 2019
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