A178118 Antidiagonal sums of the triangle A060187.

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

Author

Roger L. Bagula, May 20 2010

Keywords

• nonn

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

Crossrefs

Cf. A000800, A060187, A000045

Programs

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}]

Formula

a(n) = sum_{m=0.. floor[(n-1)/2]} A060187(n-m-1,m).

Extensions

Exact definition moved to formula - the Assoc. Eds. of the OEIS, Aug 20 2010