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

0,4

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

Links

Table of n, a(n) for n=0..22.

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

Cf. A000800, A060187, A000045

Sequence in context: A150490 A150491 A346814 * A150492 A150493 A150494

Adjacent sequences: A178115 A178116 A178117 * A178119 A178120 A178121

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