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A000428
Euler transform of A000579.
(Formerly M4519 N1913)
12
1, 8, 36, 148, 554, 2094, 7624, 27428, 96231, 332159, 1126792, 3769418, 12437966, 40544836, 130643734, 416494314, 1314512589, 4110009734, 12737116845, 39144344587, 119350793207, 361173596536, 1085171968872
OFFSET
1,2
COMMENTS
In general, if g.f. = Product_{k>=1} 1/(1-x^k)^binomial(k+m-2,m-1) and m >= 1, then log(a(n)) ~ (m+1) * Zeta(m+1)^(1/(m+1)) * (n/m)^(m/(m+1)). - Vaclav Kotesovec, Mar 12 2015
REFERENCES
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
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]
Vaclav Kotesovec, Asymptotic formula
N. J. A. Sloane, Transforms
MAPLE
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr(n-> binomial(n+5, 6)): seq(a(n), n=1..30); # Alois P. Heinz, Sep 08 2008
MATHEMATICA
nn = 30; b = Table[Binomial[n, 6], {n, 6, nn + 6}]; Rest[CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x]] (* T. D. Noe, Jun 20 2012 *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff(exp(sum(k=1, n, x^k/(1-x^k)^7/k, x*O(x^n))), n)) /* Joerg Arndt, Apr 16 2010 */
KEYWORD
nonn
STATUS
approved