A257200 a(n) = n*(n+1)*(n+2)*(n+3)*(n^2+3*n+26)/720.

1, 6, 22, 63, 154, 336, 672, 1254, 2211, 3718, 6006, 9373, 14196, 20944, 30192, 42636, 59109, 80598, 108262, 143451, 187726, 242880, 310960, 394290, 495495, 617526, 763686, 937657, 1143528, 1385824, 1669536, 2000152, 2383689, 2826726, 3336438, 3920631, 4587778, 5347056, 6208384, 7182462

Offset: 1

Author

Luciano Ancora, Apr 18 2015

Keywords

• nonn
• easy

Comments

Antidiagonal sums of the array of 4-dimensional solid numbers shown in Table 3 of Sardelis and Valahas paper (see also Example field).

See A257199 (second comment) for the general formula of this type of numbers: the sequence correspond to the case j = 4.

Binomial transform of (1, 5, 11, 14, 11, 5, 1, 0, 0, 0, ...). - Gary W. Adamson, Aug 26 2015

Examples

			Array in Comments begins:
1,  5, 15,  35,  70, 126, 210,  330, ...
1,  6, 20,  50, 105, 196, 336,  540, ...
1,  7, 25,  65, 140, 266, 462,  750, ...
1,  8, 30,  80, 175, 336, 588,  960, ...
1,  9, 35,  95, 210, 406, 714, 1170, ...
1, 10, 40, 110, 245, 476, 840, 1380, ...
		

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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A257199, A257201.

See A080852 for another version of the array.

Programs

Magma

[n*(n+1)*(n+2)*(n+3)*(n^2+3*n+26)/720: n in [1..40]]; // Vincenzo Librandi, Apr 18 2015

Mathematica

Table[n (n + 1) (n + 2) (n + 3) (n^2 + 3n + 26)/720, {n, 40}]

PARI

first(m)=vector(m,i,i*(i+1)*(i+2)*(i+3)*(i^2+3*i+26)/720) \\ Anders Hellström, Aug 26 2015

PARI

Vec(x*(-1 + x - x^2)/(-1 + x)^7 + O(x^40)) \\ Michel Marcus, Aug 27 2015

Formula

G.f.: x*(-1 + x - x^2)/(-1 + x)^7.