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 A005758 Number of partitions of n into parts of 12 kinds. (Formerly M4854) 7
 1, 12, 90, 520, 2535, 10908, 42614, 153960, 521235, 1669720, 5098938, 14931072, 42124380, 114945780, 304351020, 784087848, 1970043621, 4837060800, 11626305640, 27398234760, 63388751544, 144156086776, 322590526350 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Euler transform of A010851. - Alois P. Heinz, Oct 17 2008 Convolution square of A005758 = A006922: (1, 24, 324, 3200, 25650, ...). - Gary W. Adamson, Jun 13 2009 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 (first 201 terms from T. D. Noe) Roland Bacher, P. De La Harpe, Conjugacy growth series of some infinitely generated groups. 2016, hal-01285685v2. N. J. A. Sloane, Transforms FORMULA G.f.: Product ( 1 - x^k )^(-12). Expansion of q^(1/2) * eta(q)^-12 in powers of q. - Michael Somos, Mar 07 2012 Convolution inverse of A000735. a(n) ~ exp(2 * Pi * sqrt(2*n)) / (2^(15/4) * n^(15/4)). - Vaclav Kotesovec, Feb 28 2015 a(0) = 1, a(n) = (12/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 26 2017 G.f.: exp(12*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018 EXAMPLE G.f. = 1 + 12*x + 90*x^2 + 520*x^3 + 2535*x^4 + 10908*x^5 + 42614*x^6 + ... G.f. = 1/q + 12*q + 90*q^3 + 520*q^5 + 2535*q^7 + 10908*q^9 + 42614*q^11 + ... MAPLE with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*12, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008 MATHEMATICA CoefficientList[Series[1/QPochhammer[x, x]^12, {x, 0, 30}], x]  (* Harvey P. Dale, Apr 21 2011 *) PROG (PARI) {a(n) = if( n<0, 0, polcoeff( 1 / eta(x + x * O(x^n))^12, n))}; /* Michael Somos, Mar 07 2012 */ CROSSREFS 12th column of A144064. - Alois P. Heinz, Oct 17 2008 Cf. A006922. - Gary W. Adamson, Jun 13 2009 Sequence in context: A203636 A121590 A186209 * A084485 A130072 A135158 Adjacent sequences:  A005755 A005756 A005757 * A005759 A005760 A005761 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified February 18 03:33 EST 2020. Contains 332006 sequences. (Running on oeis4.)