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A178118
Antidiagonal sums of the triangle A060187.
1
0, 1, 1, 2, 7, 25, 100, 469, 2481, 14406, 90995, 621553, 4561112, 35736921, 297435521, 2618575194, 24297706927, 236870849417, 2419213831452, 25820011544781, 287327296473585, 3326999636488190, 40011485288491131
OFFSET
0,4
COMMENTS
This sequence is an analog to the Lucas formula which obtains A000045 as the antidiagonal sums of the Pascal triangle A007318.
REFERENCES
David M. Burton, Elementary number theory, McGraw Hill (2002), page 286
FORMULA
a(n) = sum_{m=0.. floor[(n-1)/2]} A060187(n-m-1,m).
MATHEMATICA
p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]]
a[n_] := Sum[f[n - m - 1, m], {m, 0, Floor[(n - 1)/2]}]
Table[a[n], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 20 2010
EXTENSIONS
Exact definition moved to formula - the Assoc. Eds. of the OEIS, Aug 20 2010
STATUS
approved