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 A119441 Distribution of A063834 in Abramowitz and Stegun order. 5
 1, 2, 1, 3, 2, 1, 5, 3, 4, 2, 1, 7, 5, 6, 3, 4, 2, 1, 11, 7, 10, 9, 5, 6, 8, 3, 4, 2, 1, 15, 11, 14, 15, 7, 10, 9, 12, 5, 6, 8, 3, 4, 2, 1, 22, 15, 22, 21, 25, 11, 14, 15, 20, 18, 7, 10, 9, 12, 16, 5, 6, 8, 3, 4, 2, 1, 30, 22, 30, 33, 35, 15, 22, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. FORMULA T(n,k) = product_{p=1..A036043(n,k)} A000041(c), 1<=k<=A000041(n), where c are the parts in the k-th partition of n. - R. J. Mathar, Jul 12 2013 EXAMPLE 1; 2, 1; 3, 2, 1; 5, 3, 4, 2, 1; 7, 5, 6, 3, 4, 2, 1; T(5,2) = 5 because the second partition of 5 is 1+4 and 4 can be repartitioned in 5 different ways. T(5,3) = 6 because the third partition of 5 is 2+3, where the 2 can be partitioned in 2 ways (2, 1+1) and the 3 can be partitioned in 3 ways (3, 1+2, 1+1+1), 6=2*3. T(5,4) = 3 because the fourth partition of 5 is 1+1+3 and 3 can be partitioned in 3 different ways. MAPLE # Compare two partitions (list) in AS order. AScompare := proc(p1, p2)     if nops(p1) > nops(p2) then         return 1;     elif nops(p1) < nops(p2) then         return -1;     else         for i from 1 to nops(p1) do             if op(i, p1) > op(i, p2) then                 return 1;             elif op(i, p1) < op(i, p2) then                 return -1;             end if;         end do:         return 0 ;     end if; end proc: # Produce list of partitions in AS order ASPrts := proc(n)     local pi, insrt, p, ex ;     pi := [] ;     for p in combinat[partition](n) do         insrt := 0 ;         for ex from 1 to nops(pi) do             if AScompare(p, op(ex, pi)) > 0 then                 insrt := ex ;             end if;         end do:         if nops(pi) = 0 then             pi := [p] ;         elif insrt = 0 then             pi := [p, op(pi)] ;         elif insrt = nops(pi) then             pi := [op(pi), p] ;         else             pi := [op(1..insrt, pi), p, op(insrt+1..nops(pi), pi)] ;         end if;     end do:     return pi ; end proc: A119441 := proc(n, k)     local pi, a, p ;     pi := ASPrts(n)[k] ;     a := 1 ;     for p in pi do         a := a*combinat[numbpart](p) ;     end do:     a ; end proc: for n from 1 to 10 do     for k from 1 to A000041(n) do         printf("%d, ", A119441(n, k)) ;     end do:     printf("\n") ; end do: # R. J. Mathar, Jul 12 2013 CROSSREFS Cf. A063834, A119442, A000041 (row lengths and also first column) Sequence in context: A304100 A179314 A204927 * A322083 A058399 A209434 Adjacent sequences:  A119438 A119439 A119440 * A119442 A119443 A119444 KEYWORD easy,nonn,tabf AUTHOR Alford Arnold, May 19 2006 STATUS approved

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Last modified June 25 21:43 EDT 2019. Contains 324357 sequences. (Running on oeis4.)