A367853 Expansion of e.g.f. 1/(1 - x + log(1 - 4*x)/4).

1, 2, 12, 128, 1952, 38464, 926336, 26323968, 861419520, 31882358784, 1316275003392, 59954841649152, 2985997926727680, 161401148097036288, 9408988894966579200, 588381964243109412864, 39285329204482179858432, 2789234068575581984784384

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 4^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A052820, A367851, A367852.

Cf. A352071, A355112, A367847.

Sequence in context: A214431 A227461 A367374 * A228608 A097629 A259267

Adjacent sequences: A367850 A367851 A367852 * A367854 A367855 A367856

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved