This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238439 Number of pairs (C,D) where C is a composition of u, D is a composition into distinct parts of v, and u + v = n. 2
 1, 2, 4, 10, 20, 42, 90, 182, 370, 748, 1526, 3060, 6156, 12344, 24748, 49654, 99392, 198966, 398166, 796658, 1593694, 3188584, 6377714, 12756888, 25515312, 51033092, 102068728, 204141754, 408292220, 816590586, 1633192578, 3266399030, 6532817194, 13065657556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is one possible "overcomposition" analog of overpartitions (see A015128), as overpartitions are pairs of partitions and partitions into distinct parts. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: C(x) * D(x) where C(x) and D(x) are respectively g.f. of A011782 and A032020. a(n) ~ c * 2^n, where c = 1.521048571756660822618351147397515199378647451699288... . - Vaclav Kotesovec, Apr 13 2017 MAPLE c:= proc(n) c(n):= ceil(2^(n-1)) end: b:= proc(n, i) b(n, i):= `if`(n=0, 1, `if`(i<1, 0,     expand(b(n, i-1)+`if`(i>n, 0, x*b(n-i, i-1))))) end: d:= proc(n) d(n):= (p-> add(i!*coeff(p, x, i),             i=0..degree(p)))(b(n\$2)) end: a:= proc(n) a(n):= add(c(i)*d(n-i), i=0..n) end: seq(a(n), n=0..35);  # Alois P. Heinz, Feb 28 2014 MATHEMATICA With[{N=66}, s=((1-q)*Sum[q^(n*(n+1)/2)*n!/QPochhammer[q, q, n], {n, 0, N}] )/(1-2*q)+O[q]^N; CoefficientList[s, q]] (* Jean-François Alcover, Jan 17 2016, adapted from PARI *) PROG (PARI) N=66;  q='q+O('q^N); gfc=(1-q)/(1-2*q); \\ A011782 gfd=sum(n=0, N, n!*q^(n*(n+1)/2) / prod(k=1, n, 1-q^k ) ); \\ A032020 Vec( gfc * gfd ) CROSSREFS Cf. A236002. Sequence in context: A167193 A026666 A325508 * A121880 A094536 A323445 Adjacent sequences:  A238436 A238437 A238438 * A238440 A238441 A238442 KEYWORD nonn AUTHOR Joerg Arndt, Feb 27 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 18:22 EDT 2019. Contains 328187 sequences. (Running on oeis4.)