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Search: id:A001982
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| A001982 |
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Number of partitions of 4n-1 into n nonnegative integers each no greater than 8.
(Formerly M3441 N1396)
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+0
1
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| 1, 4, 12, 31, 71, 147, 285, 519, 902, 1502, 2417, 3768, 5722, 8481, 12310, 17528, 24537, 33814, 45949, 61629, 81688, 107089, 138979, 178669, 227703, 287828, 361075, 449731, 556423, 684089, 836078, 1016110, 1228391, 1477573, 1768875
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In Cayley's terminology, this is the number of literal terms of degree n and of weight 4n-1 involving the letters a, b, c, d, e, f, g, h, i, having weights 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, p. 276-281.
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LINKS
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A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, p. 276-281.
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FORMULA
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Coefficient of x^w*z^n in the expansion of 1/((1-z)(1-xz)(1-x^2z)(1-x^3z)(1-x^4z)(1-x^5z)(1-x^6z)(1-x^7z)(1-x^8z)), where w=4n-1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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PROGRAM
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(PARI) f=1/((1-z)*(1-x*z)*(1-x^2*z)*(1-x^3*z)*(1-x^4*z)*(1-x^5*z)*(1-x^6*z)*(1-x^7*z)*(\ 1-x^8*z)); n=400; p=subst(subst(f, x, x+x*O(x^n)), z, z+z*O(z^n)); for(d=1, 60, w=4*d-1; print1(polcoeff(polcoeff(p, w), d)", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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CROSSREFS
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Cf. A001981.
Sequence in context: A005289 A037255 A027658 this_sequence A129707 A133546 A152527
Adjacent sequences: A001979 A001980 A001981 this_sequence A001983 A001984 A001985
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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