A229112 Row sums of triangle A166884.

1, 2, 6, 28, 199, 1945, 24284, 369007, 6606841, 136189033, 3176299055, 82687352399, 2376681846391, 74755785129007, 2554042404290937, 94185081322401217, 3728691027764891142, 157729043279607820306, 7100056927514281702122, 338867203461763515919479

Offset

0,2

Comments

Triangle A166884 transforms diagonals in the table of coefficients of successive iterations of x+x^2+x^3 (cf. A166880).

Links

Table of n, a(n) for n=0..19.

Example

 Triangle A166884 begins:
1;
1, 1;
3, 2, 1;
15, 9, 3, 1;
114, 62, 18, 4, 1;
1159, 593, 157, 30, 5, 1;
14838, 7266, 1812, 316, 45, 6, 1;
229401, 108720, 25989, 4271, 555, 63, 7, 1; ...
of which the row sums form this sequence.

Prog

 (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])}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A166884.

Sequence in context: A008964 A356577 A058128 * A201959 A216187 A178446

Adjacent sequences: A229109 A229110 A229111 * A229113 A229114 A229115

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2013

Status

approved