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A394268
a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n,k) * (k+2)^(2*(n-k)) * a(k).
0
1, 4, 56, 1780, 103392, 9649124, 1329514816, 254821480596, 65007836211200, 21338249088447172, 8773188839240702976, 4420903536219867238964, 2681689186158020996263936, 1928808495621762281052315300, 1623929501686280964991180439552
OFFSET
0,2
LINKS
FORMULA
log(1+4*x) = Sum_{k>=1} a(k)/k * (x/(1 + (k+2)^2*x))^k.
1 = Sum_{k>=0} a(k) * binomial(k+m-1,k) * x^k/(1 + (k+2)^2*x)^(k+m) for m >= 1.
1 = Sum_{k>=0} a(k) * x^k/k! * exp(-(k+2)^2*x).
CROSSREFS
Column k=2 of A082169.
Sequence in context: A261747 A111849 A009159 * A013055 A243486 A322733
KEYWORD
nonn,new
AUTHOR
Seiichi Manyama, Apr 11 2026
STATUS
approved