|
%I #30 Mar 25 2023 11:58:52
%S 1,2,9,52,425,4206,50737,708464,11350257,204171130,4084757561,
%T 89849981772,2156575777369,56068679418662,1569955094823585,
%U 47098171778191816,1507149193966389857,51242941744764975474
%N Row sums of A110321, a number triangle related to the Jacobsthal numbers.
%C Row sums of number triangle A110321.
%H Vincenzo Librandi, <a href="/A110322/b110322.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(x)/(1-x-2*x^2).
%F a(n) = Sum_{k=0..n} n!*J(n-k+1)/k! where J(n)=A001045(n).
%F a(n) = Sum_{k=0..n} binomial(n, k)*k!*J(k+1) where J(n)=A001045(n).
%F a(n) ~ n!*2^(n+1)*exp(1/2)/3. - _Vaclav Kotesovec_, Oct 18 2012
%F Conjecture: a(n) +(-n-1)*a(n-1) -(2*n-1)*(n-1)*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Nov 11 2014
%F a(n) - n*a(n-1) - 2*n*(n-1)*a(n-2) - 1 = 0. - _Martin Clever_, Mar 22 2023
%F a(n) = (2*e^(1/2)*2^n*Gamma(n+1,1/2)+e^-1*(-1)^n*Gamma(n+1,-1))/3. - _Martin Clever_, Mar 25 2023
%t CoefficientList[Series[E^x/(1-x-2*x^2), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 18 2012 *)
%Y Cf. A001045, A110321.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jul 20 2005
|
