A257201 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n^2+4*n+37)/5040.

1, 7, 29, 92, 246, 582, 1254, 2508, 4719, 8437, 14443, 23816, 38012, 58956, 89148, 131784, 190893, 271491, 379753, 523204, 710930, 953810, 1264770, 1659060, 2154555, 2772081, 3535767, 4473424, 5616952, 7002776, 8672312, 10672464, 13056153, 15882879, 19219317, 23139948, 27727726, 33074782, 39283166, 46465628

Offset: 1

Author

Luciano Ancora, Apr 18 2015

Keywords

• nonn
• easy

Comments

Antidiagonal sums of the array of 5-dimensional solid numbers (see Example field).

See A257199 (second comment) for the general formula of this type of numbers: the sequence correspond to the case j = 5.

The sequence is the binomial transform of (1, 6, 16, 25, 25, 16, 6, 1, 0, 0, 0, ...). - Gary W. Adamson, Aug 26 2015

Examples

			Array in Comments begins:
  1,  6, 21,  56, 126,  252,  462,  792, 1287, 2002, ...
  1,  7, 27,  77, 182,  378,  714, 1254, 2079, 3289, ...
  1,  8, 33,  98, 238,  504,  966, 1716, 2871, 4576, ...
  1,  9, 39, 119, 294,  630, 1218, 2178, 3663, 5863, ...
  1, 10, 45, 140, 350,  756, 1470, 2640, 4455, 7150, ...
  1, 11, 51, 161, 406,  882, 1722, 3102, 5247, 8437, ...
  1, 12, 57, 182, 462, 1008, 1974, 3564, 6039, 9724, ...
  ...
		

Links

• D. A. Sardelis and T. M. Valahas, On Multidimensional Pythagorean Numbers, arXiv:0805.4070 [math.GM], 2008.
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A257199, A257200.

Programs

Magma

[n*(n+1)*(n+2)*(n+3)*(n+4)*(n^2+4*n+37)/5040: n in [1..40]]; // Vincenzo Librandi, Apr 18 2015

Mathematica

Table[n (n + 1) (n + 2) (n + 3) (n + 4) (n^2 + 4n + 37)/5040, {n, 40}]

Formula

G.f.: x*(1 - x + x^2)/(1 - x)^8.