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A229112 Row sums of triangle A166884.

%I A229112 #6 Aug 16 2024 18:55:09
%S A229112 1,2,6,28,199,1945,24284,369007,6606841,136189033,3176299055,
%T A229112 82687352399,2376681846391,74755785129007,2554042404290937,
%U A229112 94185081322401217,3728691027764891142,157729043279607820306,7100056927514281702122,338867203461763515919479
%N A229112 Row sums of triangle A166884.
%C A229112 Triangle A166884 transforms diagonals in the table of coefficients of successive iterations of x+x^2+x^3 (cf. A166880).
%e A229112 Triangle A166884 begins:
%e A229112 1;
%e A229112 1, 1;
%e A229112 3, 2, 1;
%e A229112 15, 9, 3, 1;
%e A229112 114, 62, 18, 4, 1;
%e A229112 1159, 593, 157, 30, 5, 1;
%e A229112 14838, 7266, 1812, 316, 45, 6, 1;
%e A229112 229401, 108720, 25989, 4271, 555, 63, 7, 1; ...
%e A229112 of which the row sums form this sequence.
%o A229112 (PARI) {a(n, k)=local(F=x, M, N, P, m=max(n, k), A166884); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, x+x^2+x^3+x*O(x^(m+2)))); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); A166884=P~*(N~)^-1;sum(k=0,n,A166884[n+1, k+1])}
%o A229112 for(n=0, 25, print1(a(n), ", "))
%Y A229112 Cf. A166884.
%K A229112 nonn
%O A229112 0,2
%A A229112 _Paul D. Hanna_, Sep 13 2013