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A129695 Laguerre transform of the Jacobsthal numbers. 1
0, 1, 5, 30, 221, 1936, 19587, 223924, 2846741, 39763152, 604552571, 9929914204, 175116159429, 3298466345656, 66063837734819, 1401515958032628, 31386104948551253, 739730654456796832, 18299498906318500683, 474007927812558263308, 12828197342517251892485 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..440

FORMULA

a(n) = Sum_{k=0..n} C(n,k)*n!*A001045(k)/k!.

a(n) = (n!/3)*( LaguerreL(n,-2) - LaguerreL(n,1) ).

Conjecture: a(n) +(-4*n+3)*a(n-1) +(6*n^2-16*n+9)*a(n-2) -(4*n-7)*(n-2)^2*a(n-3) +(n-2)^2*(n-3)^2*a(n-4)=0. - R. J. Mathar, Feb 23 2015

a(n) ~ n^(n + 1/4) / (3*2^(3/4) * exp(n-2*sqrt(2*n)+1)) * (1 + 67/(48*sqrt(2*n))). - Vaclav Kotesovec, Nov 13 2017

MAPLE

A129695 := proc(n)

    add(binomial(n, k)*n!*A001045(k)/k!, k=0..n) ;

end proc: # R. J. Mathar, Feb 23 2015

MATHEMATICA

Table[n!*(LaguerreL[n, -2] - LaguerreL[n, 1])/3, {n, 0, 20}] (* Vaclav Kotesovec, Nov 13 2017 *)

a[n_] := Sum[n!*Binomial[n, k]*((2^k -(-1)^k)/3)/k!, {k, 0, n}]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, May 14 2018 *)

PROG

(PARI) for(n=0, 30, print1(sum(k=0, n, n!*binomial(n, k)*((2^k -(-1)^k)/3)/k!), ", ")) \\ G. C. Greubel, May 14 2018

(MAGMA) [(&+[Factorial(n)*Binomial(n, k)*((2^k -(-1)^k)/3)/Factorial(k) : k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 14 2018

CROSSREFS

Cf. A001045, A105277.

Sequence in context: A260351 A058247 A137965 * A110521 A167892 A144498

Adjacent sequences:  A129692 A129693 A129694 * A129696 A129697 A129698

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 01 2007

EXTENSIONS

Terms a(17) onward added by G. C. Greubel, May 14 2018

STATUS

approved

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Last modified August 20 14:38 EDT 2018. Contains 313918 sequences. (Running on oeis4.)