A207648 Expansion of e.g.f. Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} ((1+x)^(n+k) - 1).
1, 1, 5, 60, 1192, 34790, 1378380, 70445130, 4478636736, 344722776048, 31454679473280, 3345722335272240, 409180573835161920, 56883771843543627840, 8902319140111902785280, 1555438839901675382253600, 301239031844599064651635200, 64260075520580099615272097280
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + x + 5*x^2/2! + 60*x^3/3! + 1192*x^4/4! + 34790*x^5/5! +... such that, by definition, A(x) = 1 + ((1+x)^2-1)/2! + ((1+x)^3-1)*((1+x)^4-1)/3! + ((1+x)^4-1)*((1+x)^5-1)*((1+x)^6-1)/4! + ((1+x)^5-1)*((1+x)^6-1)*((1+x)^7-1)*((1+x)^8-1)/5! +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..275
Crossrefs
Cf. A207649.
Programs
-
PARI
{a(n)=n!*polcoeff(sum(m=0,n,1/(m+1)!*prod(k=1,m,(1+x)^(m+k)-1 +x*O(x^n)) ),n)} for(n=0,25,print1(a(n),", "))
Formula
E.g.f.: Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} ((1+x)^(n+k) - 1).
Comments