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A097809 a(n) = 5*2^n-2*n-4. 3
1, 4, 12, 30, 68, 146, 304, 622, 1260, 2538, 5096, 10214, 20452, 40930, 81888, 163806, 327644, 655322, 1310680, 2621398, 5242836, 10485714, 20971472, 41942990, 83886028, 167772106, 335544264, 671088582, 1342177220, 2684354498 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rows sums of the infinite triangle defined by T(n,n)=1, T(n,0)=n*(n+1)+1 for n=0, 1, 2, ... and interior terms defined by the Pascal-type recurrence T(n,k) = T(n-1,k-1) +T(n-1,k): sum_{k=0..n} T(n,k) = a(n). T is apparently obtained by deleting the first two columns of A129687. - J. M. Bergot, Feb 23 2013

REFERENCES

Tamas Lengyel, On p-adic properties of the Stirling numbers of the first kind, Journal of Number Theory, 148 (2015) 73-94.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

G.f.: (1+x^2)/((1-x)^2*(1-2*x)).

a(n) = 2*a(n-1)+2*n, n>0.

a(0)=1, a(1)=4, a(2)=12, a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3).

MATHEMATICA

s=1; lst={s}; Do[s+=(s+=n); AppendTo[lst, s], {n, 4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 11 2008 *)

LinearRecurrence[{4, -5, 2}, {1, 4, 12}, 30] (* Harvey P. Dale, Oct 11 2018 *)

PROG

(MAGMA) [5*2^n-2*n-4: n in [0..30]]; // Vincenzo Librandi, Feb 24 2013

CROSSREFS

Cf. A079583, A097810.

Sequence in context: A032192 A212587 A118425 * A272144 A036389 A036388

Adjacent sequences:  A097806 A097807 A097808 * A097810 A097811 A097812

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Aug 25 2004

STATUS

approved

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Last modified April 20 17:54 EDT 2019. Contains 322310 sequences. (Running on oeis4.)