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A276850 Convolution of partition polynomials of A133437 related to solutions of the Burgers-Hopf equation. 1
2, -10, 5, 42, -42, 6, 3, -168, 252, -56, -56, 7, 7, 660, -1320, 540, 360, -144, 24, 72, 8, 8, 4, 24, 72, 8, 8, 4, -2574, 6435, -3960, 1980, 495, 1485, 495, -90, 180, 90, 90, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

See the formulas dated Sep 20 2016 in OEIS A133437 for a discussion of these convolution polynomisls.

LINKS

Table of n, a(n) for n=3..43.

EXAMPLE

The first few partition polynomials are

P(1) = 0

P(2) = 0

P(3,u2) = 2 (2')^2

P(4,u2,u3) = -10 (2')^3 + 5 (2')(3')

P(5,u2,u3,u4) = 42 (2')^4 - 42 (1') (2')^2 (3') + 6 (2') (4') + 3 (3')^2

P(6,u2,..,u5) = -168 (2')^5 + 252 (2')^3 (3') - 56 (2') (3')^2 - 56 (2')^2 (4') + 7 (2')(5') + 7 (3')(4')

P(7,u2,..,u6) = 660 (2')^6 - 1320 (2')^4 (3') +  540 (2')^2 (3')^2 + 360 (2')^3 (4') - 144 (2') (3') (4') + 24 (3')^3 + 72 (2')^2 (5') + 8 (2') (6') + 8 (3') (5') + 4 (4')^2

P(8,u2,..,u7) = -2574 (2')^7 + 6435 (2')^5 (3') - 3960 (2')^3 (3')^2 + 1980  (2')^4 (4') +  495 (2') (3')^3 + 1485 (2')^2 (3') (4') +  495 (2')^3 (5') - 90 (2') (4')^2 + 180 (2')(3')(5') + 90 (2')^2 (6') + 90 (3')^2 (4') + 9 (2')(7') + 9 (3')(6') + 9 (4')(5')

...

CROSSREFS

Cf. A133437.

Sequence in context: A114232 A070730 A082192 * A033468 A047816 A095845

Adjacent sequences:  A276847 A276848 A276849 * A276851 A276852 A276853

KEYWORD

sign

AUTHOR

Tom Copeland, Sep 21 2016

STATUS

approved

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Last modified April 9 17:32 EDT 2020. Contains 333361 sequences. (Running on oeis4.)