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A172098 Coefficients of polynomial recursion with powers n*(n-1)/2: p(x, n) = x^(n - 1)*p(x, n - 1) + p(x, n - 2) 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,24

COMMENTS

Row sums are:

{1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,...}.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

p(x, n) = x^(n - 1)*p(x, n - 1) + p(x, n - 2)

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 1, 1, 1, 1},

{1, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 3, 4, 3, 4, 3, 5, 3, 4, 3, 4, 3, 4, 4, 3, 3, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 5, 4, 5, 5, 5, 6, 5, 6, 4, 6, 4, 6, 4, 5, 4, 5, 4, 4, 4, 3, 3, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1}

MATHEMATICA

Clear[p, x, n, a];

p[x, 0] = 1; p[x, 1] = x + 1;

p[x_, n_] := p[x, n] = x^(n - 1)*p[x, n - 1] + p[x, n - 2];

a = Table[CoefficientList[p[x, n], x], {n, 0, 10}];

Flatten[a]

CROSSREFS

Sequence in context: A249622 A287656 A043286 * A204162 A266227 A043285

Adjacent sequences:  A172095 A172096 A172097 * A172099 A172100 A172101

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Jan 25 2010

STATUS

approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)