A352358 Expansion of e.g.f. 1/(1 - Sum_{k>=1} binomial(k+3,4) * x^k/k!).

1, 1, 7, 51, 509, 6390, 96036, 1684284, 33760588, 761287221, 19074162865, 525696741801, 15805694091243, 514818296979974, 18058391314446224, 678683621386945560, 27207234575709663516, 1158858397815372736601, 52263672918705232821477

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: 1/(1 - (x + 3*x^2/2 + x^3/2 + x^4/24)*exp(x)).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(k+3,4) * binomial(n,k) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(x+3*x^2/2+x^3/2+x^4/24)*exp(x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, binomial(k+3, 4)*binomial(n, k)*a(n-k)));

Crossrefs

Cf. A006153, A308946, A352357.

Cf. A000332, A346890.

Sequence in context: A246572 A230883 A304939 * A293073 A368286 A081216

Adjacent sequences: A352355 A352356 A352357 * A352359 A352360 A352361

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2022

Status

approved