A364432 G.f. satisfies A(x) = 1 + x*A(x)*(2 + A(x)^3).

1, 3, 18, 162, 1728, 20169, 249318, 3207600, 42500700, 576012060, 7947785448, 111269613006, 1576658688480, 22568473199358, 325855352769588, 4740157737123696, 69405108247439676, 1022070746845708740, 15127922880893671704, 224931239520535651464

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