The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A346490 Total number of partitions of all n-multisets {1,2,...,n-j,1,2,...,j} for 0 <= j <= n. 4
 1, 2, 6, 18, 61, 228, 926, 4126, 19688, 101582, 556763, 3258810, 20134527, 131591030, 902915694, 6506096000, 48986713992, 385159376478, 3151457714098, 26806601933838, 236457090358459, 2160451562170100, 20408176433186475, 199086685731569740, 2002713693735431017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also total number of factorizations of Product_{i=1..n-j} prime(i) * Product_{i=1..j} prime(i) for 0 <= j <= n. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..576 FORMULA a(n) = Sum_{j=0..n} A001055(A002110(n-j)*A002110(j)). a(n) = Sum_{j=0..n} A346500(n-j,j). MAPLE b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*binomial(n-1, j-1), j=1..n)) end: A:= proc(n, k) option remember; `if`(n add(A(n-j, j), j=0..n): seq(a(n), n=0..24); MATHEMATICA b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Binomial[n - 1, j - 1], {j, 1, n}]]; A[n_, k_] := A[n, k] = If[n < k, A[k, n], If[k == 0, b[n], (A[n + 1, k - 1] + Sum[A[n - k + j, j] *Binomial[k - 1, j], {j, 0, k - 1}] + A[n, k - 1])/2]]; a[n_] := Sum[A[n - j, j], {j, 0, n}]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Mar 12 2022, after Alois P. Heinz *) CROSSREFS Antidiagonal sums of A346500. Cf. A001055, A002110, A346428, A346518. Sequence in context: A148462 A123639 A228448 * A177473 A177471 A303117 Adjacent sequences: A346487 A346488 A346489 * A346491 A346492 A346493 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 19 2021 STATUS approved

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

Last modified June 17 18:36 EDT 2024. Contains 373463 sequences. (Running on oeis4.)