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A110322 Row sums of a number triangle related to the Jacobsthal numbers. 3
1, 2, 9, 52, 425, 4206, 50737, 708464, 11350257, 204171130, 4084757561, 89849981772, 2156575777369, 56068679418662, 1569955094823585, 47098171778191816, 1507149193966389857, 51242941744764975474 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A330200 A143922 A305304 * A161631 A121678 A124347

Adjacent sequences:  A110319 A110320 A110321 * A110323 A110324 A110325

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 20 2005

STATUS

approved

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Last modified June 13 12:57 EDT 2021. Contains 344997 sequences. (Running on oeis4.)