A355422 Expansion of e.g.f. exp(Sum_{k=1..4} (exp(k*x) - 1)).

1, 10, 130, 2000, 35054, 684000, 14628190, 338990000, 8438270014, 224070580800, 6311530677150, 187702155610000, 5870416574854974, 192423935736656800, 6591135679171866910, 235315671951948070000, 8736534653549465359934

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (1 + 2^k + 3^k + 4^k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, 4, exp(k*x)-1))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1+2^j+3^j+4^j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Column k=4 of A355423.

Cf. A004702, A306028.

Sequence in context: A067313 A104130 A327810 * A051607 A292119 A113386

Adjacent sequences: A355419 A355420 A355421 * A355423 A355424 A355425

Keyword

nonn

Author

Seiichi Manyama, Jul 01 2022

Status

approved