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A027041 a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027023. 2
1, 2, 5, 20, 77, 306, 1209, 4656, 17713, 66618, 248025, 916020, 3359789, 12250026, 44435997, 160466304, 577185745, 2068826290, 7392167585, 26338879556, 93609302941, 331924381218, 1174482354493, 4147807582672, 14622567051025, 51466158436298, 180869949252245, 634753692067716 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

MAPLE

T:= proc(n, k) option remember;

      if k<3 or k=2*n then 1

    else add(T(n-1, k-j), j=1..3)

      fi

    end:

seq(add(T(n, k)*T(n, 2*n-k), k=0..n), n=0..30); # G. C. Greubel, Nov 04 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]; Table[Sum[T[n, k]*T(n, 2*n-k), {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Nov 04 2019 *)

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (k<3 or k==2*n): return 1

    else: return sum(T(n-1, k-j) for j in (1..3))

[sum(T(n, k)*T(n, 2*n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 04 2019

CROSSREFS

Sequence in context: A189734 A221678 A297350 * A186767 A009737 A280624

Adjacent sequences:  A027038 A027039 A027040 * A027042 A027043 A027044

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Sean A. Irvine, Oct 22 2019

STATUS

approved

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Last modified May 18 13:38 EDT 2021. Contains 343995 sequences. (Running on oeis4.)