A182017 Row square-sums of triangle A182013.

1, 5, 29, 165, 1020, 6606, 44805, 314299, 2266834, 16714004, 125501364, 956725836, 7387322749, 57669478609, 454492588153, 3611698593169, 28911762536992, 232949503809562, 1887883708627582, 15380196764853214, 125893997550676627, 1034945699861044243

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} (Sum_{i=k..n} M(i))^2, where the M(n)'s are the Motzkin numbers (A001006).

Mathematica

M[n_]:=If[n==0, 1, Coefficient[(1+x+x^2)^(n+1), x^n]/(n+1)]; Table[Sum[Sum[M[i], {i, k, n}]^2, {k, 0, n}], {n, 0, 40}]

Prog

(Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)), x^n)/(n+1);
makelist(sum(sum(M(i), i, k, n)^2, k, 0, n), n, 0, 20);

Crossrefs

Cf. A001006, A182013.

Sequence in context: A146178 A272751 A015537 * A291017 A141812 A227206

Adjacent sequences: A182014 A182015 A182016 * A182018 A182019 A182020

Keyword

nonn

Author

Emanuele Munarini, Apr 06 2012

Status

approved