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A171457 Coefficients of recursive polynomials with powers n(n-1)/2: p(x, n) = p(x, n - 1)*Sum[x^i, {i, 0, n - 1}]-x*Sum[x^i, {i, 0, n*(n - 1)/2 - 2}] 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 3, 6, 8, 8, 8, 6, 3, 1, 1, 1, 1, 4, 10, 18, 26, 33, 38, 38, 33, 26, 18, 10, 4, 1, 1, 1, 1, 5, 15, 33, 59, 92, 129, 166, 195, 211, 211, 195, 166, 129, 92, 59, 33, 15, 5, 1, 1, 1, 1, 6, 21, 54, 113, 205, 334, 499, 693, 899, 1095, 1257, 1364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Row sums are:

{1, 2, 4, 11, 46, 262, 1814, 14485, 130330, 1303256,....}.

Duplicates the first four terms of A008406.

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.

LINKS

Table of n, a(n) for n=1..77.

FORMULA

p(x, n) = p(x, n - 1)*Sum[x^i, {i, 0, n - 1}]-x*Sum[x^i, {i, 0, n*(n - 1)/2 - 2}]

EXAMPLE

{1},

{1, 1},

{1, 1, 1, 1},

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

{1, 1, 3, 6, 8, 8, 8, 6, 3, 1, 1},

{1, 1, 4, 10, 18, 26, 33, 38, 38, 33, 26, 18, 10, 4, 1, 1},

{1, 1, 5, 15, 33, 59, 92, 129, 166, 195, 211, 211, 195, 166, 129, 92, 59, 33, 15, 5, 1, 1},

{1, 1, 6, 21, 54, 113, 205, 334, 499, 693, 899, 1095, 1257, 1364, 1401, 1364, 1257, 1095, 899, 693, 499, 334, 205, 113, 54, 21, 6, 1, 1},

{1, 1, 7, 28, 82, 195, 400, 734, 1233, 1925, 2823, 3912, 5148, 6458, 7746, 8905, 9828, 10424, 10630, 10424, 9828, 8905, 7746, 6458, 5148, 3912, 2823, 1925, 1233, 734, 400, 195, 82, 28, 7, 1, 1},

{1, 1, 8, 36, 118, 313, 713, 1447, 2680, 4605, 7427, 11338, 16479, 22909, 30573, 39283, 48711, 58401, 67798, 76297, 83302, 88295, 90893, 90893, 88295, 83302, 76297, 67798, 58401, 48711, 39283, 30573, 22909, 16479, 11338, 7427, 4605, 2680, 1447, 713, 313, 118, 36, 8, 1, 1}

MATHEMATICA

Clear[p, x, n, a]

p[x, 1] = 1; p[x, 2] = x + 1; p[x, 3] = x^3 + x^2 + x + 1;

p[x_, n_] := p[x, n] = p[x, n - 1]*Sum[x^i, {i, 0, n - 1}]-x*Sum[x^i, {i, 0, n*(n - 1)/2 - 2}]

a = Table[CoefficientList[p[x, n], x], {n, 1, 10}]

Flatten[a]

CROSSREFS

A008406

Sequence in context: A008406 A039735 A283761 * A129385 A217983 A096626

Adjacent sequences:  A171454 A171455 A171456 * A171458 A171459 A171460

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Dec 09 2009

STATUS

approved

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Last modified October 20 01:39 EDT 2018. Contains 316378 sequences. (Running on oeis4.)