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 A036916 a(n) = Sum_{k=0..n} binomial(2*n-2*k,n-k)^2 * binomial(n,k)^2. 3
 1, 5, 53, 761, 12661, 229705, 4410665, 88127485, 1813270645, 38158684745, 817458330553, 17767242718285, 390819348043369, 8683822363169933, 194618212789162733, 4394243766346694161, 99862206804817230965, 2282427331053360624713 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Cf. M. Petkovsek et al., A=B, Peters, p. ix. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..500 FORMULA (n - 1)*(144*n^3 - 864*n^2 + 1693*n - 1075)*n^3*a(n) - 2*(n - 1)*(2592*n^6 - 19440*n^5 + 56322*n^4 - 80296*n^3 + 60004*n^2 - 23017*n + 3580)*a(n - 1) + (42336*n^7 - 423360*n^6 + 1769838*n^5 - 4006912*n^4 + 5293968*n^3 - 4062414*n^2 + 1661406*n - 274520)*a(n - 2) - 2*(34848*n^5 - 261360*n^4 + 741842*n^3 - 984642*n^2 + 598948*n - 127215)*(n - 2)^2*a(n - 3) + 225*(144*n^3 - 432*n^2 + 397*n - 102)*(n - 2)^2*(n - 3)^2*a(n - 4) = 0 - Vladeta Jovovic, Jul 15 2004 a(n) ~ 5^(2*n+2) / (16 * (Pi*n)^(3/2)). - Vaclav Kotesovec, Mar 02 2014 MATHEMATICA Table[Sum[Binomial[2n-2k, n-k]^2 Binomial[n, k]^2, {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Mar 31 2013 *) PROG (Haskell) a036916 n = sum \$ map    (\k -> (a007318 (2*n-2*k) (n-k))^2 * (a007318 n k)^2) [0..n] -- Reinhard Zumkeller, May 24 2012 CROSSREFS Cf. A036915, A036917. Cf. A007318. Row n=4 of A275784. Sequence in context: A333096 A036910 A235371 * A118583 A090360 A123130 Adjacent sequences:  A036913 A036914 A036915 * A036917 A036918 A036919 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 24 12:11 EST 2022. Contains 350536 sequences. (Running on oeis4.)