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A319083 Coefficients of polynomials related to the D'Arcais polynomials and Dedekind's eta(q) function, triangle read by rows, T(n,k) for 0 <= k <= n. 1
1, 0, 1, 0, 3, 1, 0, 4, 6, 1, 0, 7, 17, 9, 1, 0, 6, 38, 39, 12, 1, 0, 12, 70, 120, 70, 15, 1, 0, 8, 116, 300, 280, 110, 18, 1, 0, 15, 185, 645, 885, 545, 159, 21, 1, 0, 13, 258, 1261, 2364, 2095, 942, 217, 24, 1, 0, 18, 384, 2262, 5586, 6713, 4281, 1498, 284, 27, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

FORMULA

The polynomials are defined by recurrence: p(0,x) = 1 and for n > 0 by

p(n, x) = x*Sum_{k=0..n-1} sigma(n-k)*p(k, x).

EXAMPLE

Triangle starts:

[0] 1

[1] 0,  1

[2] 0,  3,   1

[3] 0,  4,   6,   1

[4] 0,  7,  17,   9,     1

[5] 0,  6,  38,   39,   12,    1

[6] 0, 12,  70,  120,   70,   15,   1

[7] 0,  8, 116,  300,  280,  110,  18,   1

[8] 0, 15, 185,  645,  885,  545, 159,  21,  1

[9] 0, 13, 258, 1261, 2364, 2095, 942, 217, 24, 1

MAPLE

P := proc(n, x) option remember; if n = 0 then 1 else

x*add(numtheory:-sigma(n-k)*P(k, x), k=0..n-1) fi end:

Trow := n -> seq(coeff(P(n, x), x, k), k=0..n):

seq(Trow(n), n=0..9);

CROSSREFS

Row sums are A180305.

Cf. A008298, A078521, A319933.

Sequence in context: A274662 A186827 A207327 * A045406 A143468 A133728

Adjacent sequences:  A319080 A319081 A319082 * A319084 A319085 A319086

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 03 2018

STATUS

approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)