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A171456 Coefficients of recursive polynomials with powers n(n-1)/2: p(x, n) = p(x, n - 1)*Sum[x^i, {i, 0, n - 1}] 0
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 3, 6, 10, 13, 14, 13, 10, 6, 3, 1, 1, 4, 10, 20, 33, 47, 59, 66, 66, 59, 47, 33, 20, 10, 4, 1, 1, 5, 15, 35, 68, 115, 174, 239, 301, 350, 377, 377, 350, 301, 239, 174, 115, 68, 35, 15, 5, 1, 1, 6, 21, 56, 124, 239, 413, 652, 952, 1297 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Row sums are:

{1, 2, 4, 16, 80, 480, 3360, 26880, 241920, 2419200,....}

REFERENCES

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

LINKS

Table of n, a(n) for n=1..73.

FORMULA

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

EXAMPLE

{1},

{1, 1},

{1, 1, 1, 1},

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

{1, 3, 6, 10, 13, 14, 13, 10, 6, 3, 1},

{1, 4, 10, 20, 33, 47, 59, 66, 66, 59, 47, 33, 20, 10, 4, 1},

{1, 5, 15, 35, 68, 115, 174, 239, 301, 350, 377, 377, 350, 301, 239, 174, 115, 68, 35, 15, 5, 1},

{1, 6, 21, 56, 124, 239, 413, 652, 952, 1297, 1659, 2001, 2283, 2469, 2534, 2469, 2283, 2001, 1659, 1297, 952, 652, 413, 239, 124, 56, 21, 6, 1},

{1, 7, 28, 84, 208, 447, 860, 1512, 2464, 3760, 5413, 7393, 9620, 11965, 14260, 16316, 17947, 18996, 19358, 18996, 17947, 16316, 14260, 11965, 9620, 7393, 5413, 3760, 2464, 1512, 860, 447, 208, 84, 28, 7, 1},

{1, 8, 36, 120, 328, 775, 1635, 3147, 5611, 9371, 14783, 22169, 31761, 43642, 57694, 73563, 90650, 108134, 125028, 140264, 152798, 161721, 166361, 166361, 161721, 152798, 140264, 125028, 108134, 90650, 73563, 57694, 43642, 31761, 22169, 14783, 9371, 5611, 3147, 1635, 775, 328, 120, 36, 8, 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}]

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

Flatten[a]

CROSSREFS

A008406

Sequence in context: A167600 A008287 A017859 * A028356 A232244 A260644

Adjacent sequences:  A171453 A171454 A171455 * A171457 A171458 A171459

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Dec 09 2009

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)