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 A364432 G.f. satisfies A(x) = 1 + x*A(x)*(2 + A(x)^3). 3
 1, 3, 18, 162, 1728, 20169, 249318, 3207600, 42500700, 576012060, 7947785448, 111269613006, 1576658688480, 22568473199358, 325855352769588, 4740157737123696, 69405108247439676, 1022070746845708740, 15127922880893671704, 224931239520535651464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..19. FORMULA a(n) = Sum_{k=0..n} 2^(n-k) * binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1). D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +2*(-74*n^3 -375*n^2+ 665*n -252)*a(n-1) +12*(-337*n^3 +1941*n^2 -2984*n +1092)*a(n-2) +144*(-70*n^3 +861*n^2 -3347*n +4152)*a(n-3) +432*(n-4)*(31*n^2 -314*n +735)*a(n-4) -2592*(10*n-51) *(n-4)*(n-5)*a(n-5) +15552*(n-5)*(n-6) *(n-4)*a(n-6)=0. - R. J. Mathar, Jul 25 2023 MAPLE A364432 := proc(n) add(2^(n-k)* binomial(n, k) * binomial(n+3*k+1, n) / (n+3*k+1), k=0..n) ; end proc: seq(A364432(n), n=0..70); # R. J. Mathar, Jul 25 2023 PROG (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1)); CROSSREFS Cf. A047891, A348793. Cf. A364430, A364431. Sequence in context: A328030 A301371 A115415 * A065058 A032031 A127646 Adjacent sequences: A364429 A364430 A364431 * A364433 A364434 A364435 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 24 2023 STATUS approved

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Last modified August 15 01:22 EDT 2024. Contains 375171 sequences. (Running on oeis4.)