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A144400 Triangle read by rows: row n (n > 0) gives the coefficients of x^k (0 <= k <= n - 1) in the expansion of Sum_{j=0..n} A000931(j+4)*binomial(n, j)*x^(j - 1)*(1 - x)^(n - j). 3
1, 2, -1, 3, -3, 1, 4, -6, 4, 0, 5, -10, 10, 0, -3, 6, -15, 20, 0, -18, 10, 7, -21, 35, 0, -63, 70, -24, 8, -28, 56, 0, -168, 280, -192, 49, 9, -36, 84, 0, -378, 840, -864, 441, -89, 10, -45, 120, 0, -756, 2100, -2880, 2205, -890, 145, 11, -55, 165, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..59.

FORMULA

G.f.: (y - (1 - 2*x)*y^2)/(1 - 3*(1 - x)*y + (3 - 6*x + 2*x^2)*y^2 - (1 - 3*x + 2*x^2 + x^3)*y^3). - Franck Maminirina Ramaharo, Oct 22 2018

EXAMPLE

Triangle begins:

    1;

    2,  -1;

    3,  -3,   1;

    4,  -6,   4, 0;

    5, -10,  10, 0,   -3;

    6, -15,  20, 0,  -18,   10;

    7, -21,  35, 0,  -63,   70,   -24;

    8, -28,  56, 0, -168,  280,  -192,   49;

    9, -36,  84, 0, -378,  840,  -864,  441,  -89;

   10, -45, 120, 0, -756, 2100, -2880, 2205, -890, 145;

     ... reformatted. - Franck Maminirina Ramaharo, Oct 22 2018

MATHEMATICA

a[0] = 0; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3];

p[x_, n_] := Sum[a[k]*Binomial[n, k]*x^(k - 1)*(1 - x)^(n - k), {k, 0, n}];

Table[Table[Coefficient[p[x, n], x, k], {k, 0, n - 1}], {n, 1, 12}]// Flatten

CROSSREFS

Row sums: subsequence of A000931, A078027, A182097.

Cf. A122753, A123018, A123019, A123021, A123027, A123199, A123202, A123202, A123217, A123221, A141720, A144387, A174128.

Sequence in context: A093430 A074659 A131251 * A225281 A057145 A134394

Adjacent sequences:  A144397 A144398 A144399 * A144401 A144402 A144403

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 03 2008

EXTENSIONS

Edited, and new name by Franck Maminirina Ramaharo, Oct 22 2018

STATUS

approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)