The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A292190 Sum of n-th powers of products of terms in all partitions of n into distinct parts. 8
 1, 1, 4, 35, 337, 11925, 371081, 49032439, 3545396034, 3416952655320, 749189363202730, 598250899004413536, 2383502427069445040595, 1729793152213690218766715, 131751643363739706679145099315, 271212858254426215135033141804302 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..98 FORMULA a(n) = [x^n] Product_{k=1..n} (1 + k^n*x^k). EXAMPLE 5 = 4 + 1 = 3 + 2. So a(5) = 5^5 + (4*1)^5 + (3*2)^5 = 11925. MAPLE b:= proc(n, i, k) option remember; (m->       `if`(mn, 0, i^k*b(n-i, i-1, k)))))(i*(i+1)/2)     end: a:= n-> b(n\$3): seq(a(n), n=0..20);  # Alois P. Heinz, Sep 11 2017 MATHEMATICA nmax = 15; Table[SeriesCoefficient[Product[(1 + k^n*x^k), {k, 1, nmax}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Sep 12 2017 *) PROG (PARI) {a(n) = polcoeff(prod(k=1, n, 1+k^n*x^k+x*O(x^n)), n)} CROSSREFS Main diagonal of A292189. Cf. A265949, A292167, A292194, A292305, A292306. Sequence in context: A174436 A145607 A188527 * A026304 A215541 A104456 Adjacent sequences:  A292187 A292188 A292189 * A292191 A292192 A292193 KEYWORD nonn AUTHOR Seiichi Manyama, Sep 11 2017 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 April 20 18:08 EDT 2021. Contains 343135 sequences. (Running on oeis4.)