A354625 Expansion of e.g.f. (1 + x)^(x^4).
1, 0, 0, 0, 0, 120, -360, 1680, -10080, 72576, 1209600, -14256000, 159667200, -1902700800, 24458353920, -120860812800, -193037644800, 23690780467200, -646842994237440, 14916006359654400, -230812655044608000, 3182953434006528000, -37667817509059584000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x)^x^4)) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^4*log(1+x)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-(i-1)!*sum(j=5, i,(-1)^j*j/(j-4)*v[i-j+1]/(i-j)!)); v;
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PARI
a(n) = n!*sum(k=0, n\5, stirling(n-4*k, k, 1)/(n-4*k)!);
Formula
a(0) = 1; a(n) = -(n-1)! * Sum_{k=5..n} (-1)^k * k/(k-4) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/5)} Stirling1(n-4*k,k)/(n-4*k)!.