login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A228997
Total sum of the 7th powers of lengths of ascending runs in all permutations of [n].
3
0, 1, 130, 2706, 32226, 315684, 2961498, 28544040, 291590754, 3194874900, 37656861354, 477018980928, 6477756701010, 94006723773564, 1453236561824250, 23855684885059944, 414605141516228418, 7607828522859788580, 147012653519046471114, 2984603478905797978320
OFFSET
0,3
LINKS
FORMULA
E.g.f.: (exp(x)*(42*x^5+210*x^4+280*x^3+126*x-126)+x+126)/(x-1)^2.
a(n) ~ n! * (532*exp(1)+127)*n. - Vaclav Kotesovec, Sep 12 2013
MAPLE
a:= proc(n) option remember; `if`(n<4, [0, 1, 130, 2706][n+1],
((16*n^3-38*n^2-16*n+278) *a(n-1)
-(8*n^4-3*n^3-101*n^2+623*n-512) *a(n-2)
+2*(n-2)*(8*n^3-32*n^2+134*n-95) *a(n-3)
-(n-2)*(n-3)*(8*n^2-37*n+44) *a(n-4)) /(8*n^2-27*n+24))
end:
seq(a(n), n=0..30);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[(Exp[x](42x^5+210x^4+280x^3+126x-126)+x+126)/(x-1)^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 31 2021 *)
CROSSREFS
Column k=7 of A229001.
Sequence in context: A239094 A084641 A271758 * A168124 A224169 A223860
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2013
STATUS
approved