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A027042 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027023. 2
1, 4, 11, 52, 225, 920, 3695, 14464, 55593, 210776, 789995, 2933380, 10807625, 39556316, 143958335, 521340016, 1879901265, 6753038624, 24176722555, 86294777316, 307179518193, 1090771084252, 3864614381391, 13664531314176, 48225146757337, 169905685271956, 597661852713467 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..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-1), n=1..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-1}], {n, 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-1)) for n in (1..30)] # G. C. Greubel, Nov 04 2019

CROSSREFS

Sequence in context: A318120 A218957 A149317 * A051770 A262006 A209110

Adjacent sequences:  A027039 A027040 A027041 * A027043 A027044 A027045

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.)