The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A229052 a(n) = Sum_{k=0..n} binomial(n^2-n*k, n*k-k^2) * binomial(n*k, k^2). 3
 1, 2, 6, 92, 6662, 2150552, 3093730764, 18251332286098, 466740831542894470, 47238803741195397513182, 20522607409110459026633535856, 34700017072200465774261952422246668, 250699892545838622857396499800167790109260, 6984916990466628202550631436961441381064765905022 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..50 FORMULA a(n) = Sum_{k=0..n} binomial(n^2-n*k, (n-k)^2) * binomial(n*k, k^2). a(n) = Sum_{k=0..n} A228832(n, n-k) * A228832(n, k). a(n) = Sum_{k=0..n} (n^2-n*k)! * (n*k)! / ( ((n-k)^2)! * (n*k-k^2)!^2 * (k^2)! ). a(n) ~ c * 2^(n^2+2)/(Pi*n^2), where c = EllipticTheta[3,0,1/E^2] = 1.271341522189... if n is even and c = EllipticTheta[2,0,1/E^2] = 1.23528676585389... if n is odd. - Vaclav Kotesovec, Sep 22 2013 EXAMPLE The triangle A228832(n,k) = C(n*k, k^2) illustrates the terms involved in the sum a(n) = Sum_{k=0..n} A228832(n, n-k) * A228832(n, k): 1; 1, 1; 1, 2, 1; 1, 3, 15, 1; 1, 4, 70, 220, 1; 1, 5, 210, 5005, 4845, 1; 1, 6, 495, 48620, 735471, 142506, 1; 1, 7, 1001, 293930, 30421755, 183579396, 5245786, 1; ... MATHEMATICA Table[Sum[Binomial[n^2 - n k, n k - k^2] Binomial[n k, k^2], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 22 2013 *) PROG (PARI) {a(n)=sum(k=0, n, binomial(n^2-n*k, n*k-k^2)*binomial(n*k, k^2))} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A228832, A206847, A218792. Sequence in context: A218151 A007188 A206156 * A280117 A129364 A092287 Adjacent sequences:  A229049 A229050 A229051 * A229053 A229054 A229055 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 22 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 18:15 EST 2020. Contains 338908 sequences. (Running on oeis4.)