A110542 Row sums of number triangle A110541.
1, 2, 3, 5, 9, 19, 48, 140, 458, 1635, 6272, 25580, 110130, 497832, 2352807, 11584809, 59251847, 313995514, 1720289573, 9725340014, 56636885799, 339259270680, 2087446695738, 13177129073994, 85244657070582, 564567565446106
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..690
Programs
-
Mathematica
A110542[n_] := Sum[Sum[Binomial[(k - 1)*(n - k) - (k - 2)*j, j]* Binomial[j, n - k - j], {j, 0, n - k}], {k, 0, n}]; Table[A110542[n], {n, 0, 50}] (* G. C. Greubel, Aug 31 2017 *)
-
PARI
for(n=0,20, print1(sum(k=0,n, sum(j=0,n-k, binomial((k-1)*(n-k) -(k-2)*j, j)*binomial(j, n-k-j))), ", ")) \\ G. C. Greubel, Aug 31 2017
Formula
a(n)=sum{k=0..n, sum{j=0..n-k, C((k-1)*(n-k)-(k-2)*j, j)*C(j, n-k-j)}}