A062748 -id:A062748 - cp's OEIS frontend

A124090 C(n,7)-1.

0, 7, 35, 119, 329, 791, 1715, 3431, 6434, 11439, 19447, 31823, 50387, 77519, 116279, 170543, 245156, 346103, 480699, 657799, 888029, 1184039, 1560779, 2035799, 2629574, 3365855, 4272047, 5379615, 6724519, 8347679, 10295471, 12620255

Offset: 7

Zerinvary Lajos, Nov 25 2006

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Cf. A000096, A062748, A063258, A062988.

Maple
```
[seq(binomial(n,7)-1,n=7..47)];
```

Binomial[Range[7,50],7]-1 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,7,35,119,329,791,1715,3431},40] (* Harvey P. Dale, Aug 14 2014 *)

A165618 a(n) = binomial(n+8,8) - 1.

Original entry on oeis.org

0, 8, 44, 164, 494, 1286, 3002, 6434, 12869, 24309, 43757, 75581, 125969, 203489, 319769, 490313, 735470, 1081574, 1562274, 2220074, 3108104, 4292144, 5852924, 7888724, 10518299, 13884155, 18156203, 23535819, 30260339, 38608019, 48903491

Offset: 0

Enrique Pérez Herrero, Sep 22 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
E. Pérez Herrero, Binomial Matrix (I) partitions, Psychedelic Geometry Blogspot, 09/22/09
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A000096, A000581, A062748, A063258, A062988, A124089, A124090, A035927.

Table[ -1 + Binomial[n + 8, 8], {n, 0, 30}]
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,8,44,164,494,1286,3002,6434,12869},40] (* Harvey P. Dale, Nov 18 2013 *)

vector(100,n,binomial(n+7,8)-1) \\ Charles R Greathouse IV, May 27 2011

a(n) = binomial(n+8,8) - 1 = A000581(n+8) - 1.
a(n) = Sum_{r=1..n} binomial(8,r)*binomial(n,r).
a(n) = n(n+9)(n^6 + 27n^5 + 303n^4 + 1809n^3 + 6168n^2 + 11772n + 12176)/40320.

Edited by Charles R Greathouse IV, May 27 2011

A341773 Number of partitions of 2*n into exactly n nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 0, 4, 2, 0, 4, 3, 0, 5, 4, 1, 5, 4, 1, 5, 5, 1, 6, 6, 2, 6, 6, 2, 6, 7, 3, 7, 9, 4, 8, 9, 4, 8, 10, 5, 9, 12, 6, 10, 12, 7, 10, 13, 8, 12, 15, 10, 13, 16, 11, 13, 17, 12

Offset: 0

Ilya Gutkovskiy, Feb 19 2021

nonn

David A. Corneth, Table of n, a(n) for n = 0..2999

Cf. A000292, A024692, A062748, A068980, A298269, A319799, A338586, A341774, A341775, A341776, A341777, A341778.

nmax = 80; CoefficientList[Series[Product[1/(1 - x^(Binomial[k + 4, 3] - 1)), {k, 0, nmax}], {x, 0, nmax}], x]

G.f.: Product_{k>=0} 1 / (1 - x^(binomial(k+4,3)-1)).

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A124090 C(n,7)-1.

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A165618 a(n) = binomial(n+8,8) - 1.

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A341773 Number of partitions of 2*n into exactly n nonzero tetrahedral numbers.

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