The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A336577 a(n) = Sum_{k=0..n} 2^k * binomial(n,k) * binomial(n^2+k+1,n)/(n^2+k+1). 4
 1, 3, 24, 498, 18708, 1055838, 80682414, 7829287392, 924359573112, 128815914107370, 20717986773639696, 3779867347688995698, 771666206195918154156, 174345811623642373266360, 43198501381068549879753648, 11648965476456962547182140512, 3396661425137920919866033312752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..297 FORMULA a(n) = (1/(n^2+1)) * Sum_{k=0..n} 2^(n-k) * binomial(n^2+1,k) * binomial((n+1)*n-k,n-k). a(n) ~ 3^n * exp(n + 1/6) * n^(n - 5/2) / sqrt(2*Pi). - Vaclav Kotesovec, Jul 31 2021 MATHEMATICA a[n_] := Sum[2^k * Binomial[n, k] * Binomial[n^2 + k + 1, n]/(n^2 + k + 1), {k, 0, n}];  Array[a, 17, 0] (* Amiram Eldar, Jul 27 2020 *) PROG (PARI) {a(n) = sum(k=0, n, 2^k*binomial(n, k)*binomial(n^2+k+1, n)/(n^2+k+1))} (PARI) {a(n) = sum(k=0, n, 2^(n-k)*binomial(n^2+1, k)*binomial((n+1)*n-k, n-k))/(n^2+1)} CROSSREFS Main diagonal of A336574. Cf. A336495, A336537, A336578. Sequence in context: A236466 A185970 A279165 * A194157 A166736 A330297 Adjacent sequences:  A336574 A336575 A336576 * A336578 A336579 A336580 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 26 2020 STATUS approved

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

Last modified May 21 11:28 EDT 2022. Contains 353908 sequences. (Running on oeis4.)