A110322 Row sums of A110321, a number triangle related to the Jacobsthal numbers.

1, 2, 9, 52, 425, 4206, 50737, 708464, 11350257, 204171130, 4084757561, 89849981772, 2156575777369, 56068679418662, 1569955094823585, 47098171778191816, 1507149193966389857, 51242941744764975474

Offset

0,2

Comments

Row sums of number triangle A110321.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

E.g.f.: exp(x)/(1-x-2*x^2).

a(n) = Sum_{k=0..n} n!*J(n-k+1)/k! where J(n)=A001045(n).

a(n) = Sum_{k=0..n} binomial(n, k)*k!*J(k+1) where J(n)=A001045(n).

a(n) ~ n!*2^(n+1)*exp(1/2)/3. - Vaclav Kotesovec, Oct 18 2012

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

a(n) - n*a(n-1) - 2*n*(n-1)*a(n-2) - 1 = 0. - Martin Clever, Mar 22 2023

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

Mathematica

CoefficientList[Series[E^x/(1-x-2*x^2), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* Vaclav Kotesovec, Oct 18 2012 *)

Crossrefs

Cf. A001045, A110321.

Sequence in context: A143922 A305304 A369090 * A161631 A121678 A124347

Adjacent sequences: A110319 A110320 A110321 * A110323 A110324 A110325

Keyword

easy,nonn

Author

Paul Barry, Jul 20 2005

Status

approved