login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A182017
Row square-sums of triangle A182013.
1
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
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
Sequence in context: A146178 A272751 A015537 * A291017 A141812 A227206
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Apr 06 2012
STATUS
approved