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A099240 Main diagonal of A099239. 2
1, 2, 8, 41, 250, 1757, 13917, 122166, 1173662, 12222605, 136927351, 1639768418, 20880556880, 281460326864, 4000651782511, 59761935358025, 935445106491702, 15303039199768237, 261030618751031385, 4632889302298054713 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..490

FORMULA

a(n) = Sum_{j=0..n} binomial(n^2 - (n-1)*(j-1), j).

a(n) = Sum_{j=0..n} binomial(n + (n-1)*(j+1), n*(j+1) - 1) with a(0) = 1.

MATHEMATICA

Table[Sum[Binomial[n^2 -(n-1)*(j-1), j], {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Mar 09 2021 *)

PROG

(Sage) [sum(binomial(n^2 -(n-1)*(j-1), j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021

(Magma) [1] cat [(&+[Binomial(n+(n-1)*(j+1), n*(j+1)-1): j in [0..n]]): n in [1..30]]; // G. C. Greubel, Mar 09 2021

CROSSREFS

Cf. A099239.

Sequence in context: A177340 A067119 A093935 * A134055 A136281 A125698

Adjacent sequences:  A099237 A099238 A099239 * A099241 A099242 A099243

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)