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A178725 Irregular triangle read by rows: row n gives coefficients in expansion of Product_{k=1..n} (1 + x^(4*k - 1) for n >= 0. 0
1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 1, 3, 0, 0, 2, 2, 0, 0, 3, 2, 0, 1, 3, 1, 0, 1, 3, 1, 0, 2, 3, 0, 0, 2, 2, 0, 0, 3, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,57

COMMENTS

For n >= 1, row n is the Poincaré polynomial for the Lie group B_n (or, equally, Sp(2n) or O(2n+1)).

Row sums are powers of 2.

REFERENCES

Borel, A. and Chevalley, C., The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 1955, no. 14, pp 1-9.

H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.

LINKS

Table of n, a(n) for n=0..209.

EXAMPLE

Triangle begins:

[1] (the empty product)

[1, 0, 0, 1]

[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]

[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]

[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]

[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]

...

CROSSREFS

Rows: A170956-A170965. Cf. A142724.

Sequence in context: A306383 A172099 A170957 * A257402 A230263 A139354

Adjacent sequences:  A178722 A178723 A178724 * A178726 A178727 A178728

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Dec 26 2010

STATUS

approved

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Last modified June 19 00:37 EDT 2021. Contains 345125 sequences. (Running on oeis4.)