A117750 Irregular triangle which contains in row n those partition numbers A000041(n*(2m+1) + m + 2) which are congruent to 0 mod (2m+1) for 1 <= m <= n.

30, 135, 490, 2436, 1575, 10143, 4565, 37338, 1300156, 792, 12310, 124754, 1575, 31185, 386155, 26543660, 75175, 1121505, 4835271870, 5604, 173525, 3087735, 10143, 386155, 8118264, 1327710076, 4328363658647, 25025873760111

Offset

2,1

References

Robert Kanigel, The Man Who Knew Infinity, Washington Square Press, New York, 1991, page 302.

Links

Table of n, a(n) for n=2..29.

Example

The first line contains A000041(9)=30 from n=2 and m=1 and A000041(14)=135 from n=2 and m=2.
The fifth line contains A000041(29)=4565 from n=5 and m=2, A000041(40)=37338 from n=5 and m=3, and A000041(62)=1300156 from n=m=5.
The array starts
30, 135;
490, 2436;
1575, 10143;
4565, 37338, 1300156;
792, 12310, 124754;
1575, 31185, 386155, 26543660;
75175, 1121505, 4835271870;
5604, 173525, 3087735;
10143, 386155, 8118264, 1327710076, 4328363658647, 25025873760111;

Mathematica

b = Table[Flatten[Table[If[Mod[a[[( 2*n + 1)*m + n + 2]], 2*n + 1] == 0, PartitionsP[(2*n + 1)*m + n + 2], {}], {n, 1, m}]], {m, 1, 10}] Flatten[b]

Crossrefs

Cf. A000041, A117749.

Sequence in context: A291582 A079588 A100147 * A348828 A158462 A064495

Adjacent sequences: A117747 A117748 A117749 * A117751 A117752 A117753

Keyword

nonn,tabf

Author

Roger L. Bagula, Apr 14 2006

Extensions

Comments and definition rephrased, offset corrected - the Assoc. Eds. of the OEIS, Jun 27 2010

Status

approved