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A354419
Expansion of e.g.f. log(1+4*x) * exp(x)/4.
1
0, 1, -2, 23, -276, 4509, -91190, 2205587, -62104168, 1995807993, -72089029802, 2891304481999, -127498010037244, 6131189086886421, -319320539953144158, 17905976286288568267, -1075611833288214177232, 68909527979479961534705
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..n-1} (-4)^(n-1-k) / ((n-k) * k!).
a(0) = 0, a(1) = 1, a(n) = (-4 * n + 5) * a(n-1) + 4 * (n-1) * a(n-2) + 1.
a(n) ~ -(-1)^n * (n-1)! * 4^(n-1) / exp(1/4). - Vaclav Kotesovec, Jun 08 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(log(1+4*x)*exp(x)/4)))
(PARI) a(n) = n!*sum(k=0, n-1, (-4)^(n-1-k)/((n-k)*k!));
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; v[2]=1; for(i=2, n, v[i+1]=(-4*i+5)*v[i]+4*(i-1)*v[i-1]+1); v;
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 27 2022
STATUS
approved