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 A001982 Number of partitions of 4n-1 into n nonnegative integers each no greater than 8. (Formerly M3441 N1396) 1
 0, 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, 2108041, 2501480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 REFERENCES A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281. A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281. [Annotated scanned copy] FORMULA 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 G.f.: (x^14 +3*x^13 +5*x^12 +8*x^11 +13*x^10 +17*x^9 +19*x^8 +19*x^7 +19*x^6 +17*x^5 +13*x^4 +8*x^3 +5*x^2 +3*x+1)*x / ((x^4+x^3+x^2+x+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+x+1)^2 *(x+1)^3 *(x-1)^8). - Alois P. Heinz, Jul 25 2015 PROG (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=0, 60, w=4*d-1; print1(polcoeff(polcoeff(p, w), d)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008 CROSSREFS Cf. A001981. Sequence in context: A005289 A037255 A027658 * A129707 A320545 A232580 Adjacent sequences:  A001979 A001980 A001981 * A001983 A001984 A001985 KEYWORD nonn,easy AUTHOR EXTENSIONS Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008 a(0)=0 inserted by Alois P. Heinz, Jul 25 2015 STATUS approved

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Last modified July 13 12:30 EDT 2020. Contains 335687 sequences. (Running on oeis4.)