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A171146 The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + (2*n - 1)*x + 1)^Floor[n/2]] ( correction) 0
1, 1, 1, 1, 5, 1, 1, 6, 6, 1, 1, 18, 83, 18, 1, 1, 19, 101, 101, 19, 1, 1, 39, 510, 2275, 510, 39, 1, 1, 40, 549, 2785, 2785, 549, 40, 1, 1, 68, 1738, 19856, 86995, 19856, 1738, 68, 1, 1, 69, 1806, 21594, 106851, 106851, 21594, 1806, 69, 1, 1, 105, 4415, 93030, 985645 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, 7, 14, 121, 242, 3375, 6750, 130321, 260642, 6436343, 12872686...}.

LINKS

Table of n, a(n) for n=1..60.

FORMULA

p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + (2*n - 1)*x + 1)^Floor[n/2]]

EXAMPLE

{1},

{1, 1},

{1, 5, 1},

{1, 6, 6, 1},

{1, 18, 83, 18, 1},

{1, 19, 101, 101, 19, 1},

{1, 39, 510, 2275, 510, 39, 1},

{1, 40, 549, 2785, 2785, 549, 40, 1},

{1, 68, 1738, 19856, 86995, 19856, 1738, 68, 1},

{1, 69, 1806, 21594, 106851, 106851, 21594, 1806, 69, 1},

{1, 105, 4415, 93030, 985645, 4269951, 985645, 93030, 4415, 105, 1},

{1, 106, 4520, 97445, 1078675, 5255596, 5255596, 1078675, 97445, 4520, 106, 1}

MATHEMATICA

Clear[p, n, x, a]

p[x, 1] := 1;

p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, (x + 1)*p[x, n - 1], (x^2 + (2*n - 1)*x + 1)^Floor[n/2]];

a = Table[CoefficientList[p[x, n], x], {n, 1, 12}];

Flatten[a]

CROSSREFS

Cf. A051159 , A169623, A007318, A171142, A171143

Sequence in context: A050178 A297986 A298635 * A174038 A328098 A200401

Adjacent sequences:  A171143 A171144 A171145 * A171147 A171148 A171149

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Dec 04 2009

STATUS

approved

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Last modified January 23 12:51 EST 2022. Contains 350511 sequences. (Running on oeis4.)