|
| |
|
|
A077365
|
|
Sum of products of factorials of parts in all partitions of n.
|
|
7
| |
|
|
1, 1, 3, 9, 37, 169, 981, 6429, 49669, 430861, 4208925, 45345165, 536229373, 6884917597, 95473049469, 1420609412637, 22580588347741, 381713065286173, 6837950790434781, 129378941557961565, 2578133190722896861
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Row sums of arrays A069123 and A134133. Row sums of triangle A134134.
|
|
|
FORMULA
| G.f.: 1/Product_{m>0} (1-m!*x^m). Recurrence: a(n) = 1/n*Sum_{k=1..n} b(k)*a(n-k), where b(k) = Sum_{d divides k} d*d!^(k/d).
|
|
|
EXAMPLE
| The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1, the corresponding products of factorials of parts are 24,6,4,2,1 and their sum is a(4) = 37.
1 + x + 3 x^2 + 9 x^3 + 37 x^4 + 169 x^5 + 981 x^6 + 6429 x^7 + 49669 x^8 + ...
|
|
|
MATHEMATICA
| Table[Plus @@ Map[Times @@ (#!) &, IntegerPartitions[n]], {n, 0, 20}]
a[ n_] := If[ n < 0, 0, Plus @@ Times @@@ (IntegerPartitions[ n] !)] (* Michael Somos, Feb 09 2012 *)
|
|
|
CROSSREFS
| Cf. A006906, A074141.
Sequence in context: A134818 A002751 A119856 * A006229 A008986 A105215
Adjacent sequences: A077362 A077363 A077364 * A077366 A077367 A077368
|
|
|
KEYWORD
| nonn,changed
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 30 2002
|
|
|
EXTENSIONS
| Unnecessarily complicated mma code deleted by N. J. A. Sloane, Sep 21 2009
New Mathematica code by Olivier Gérard (olivier.gerard(AT)gmail.com), Oct 22 2011
|
| |
|
|
