0,3

Also number of planar partitions monotonically decreasing down anti-diagonals (i.e., with b(n,k)<=b(n-1,k+1)). Transpose (to get planar partitions decreasing down columns), then take the conjugate of each row. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 15 2006

D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; p. 133.

M. S. Cheema and W. E. Conway, Numerical investigation of certain asymptotic results in the theory of partitions, Math. Comp., 26 (1972), 999-1005.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G.f.: Product (1 - x^k )^{-c(k)}, c(k) = 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ....

Euler transform of A110654. - Michael Somos Sep 19 2006

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-> `if`(modp(n, 2)=0, n, n+1)/2): seq (a(n), n=0..39); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]

(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k+x*O(x^n))^-ceil(k/2)), n))} /* Michael Somos Sep 19 2006 */

Sequence in context: A079970 A079816 A100482 this_sequence A094974 A100671 A005251

Adjacent sequences: A003290 A003291 A003292 this_sequence A003294 A003295 A003296

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 06 2000. Additional comments from Michael Somos, May 19, 2000.