A362247
Expansion of e.g.f. exp(x * exp(x * (exp(x) - 1))).
Original entry on oeis.org
1, 1, 1, 7, 37, 201, 1531, 12433, 112729, 1158769, 12920311, 157007841, 2063354437, 29052921769, 436908104179, 6981843029281, 118083965782321, 2106973566128865, 39538081855597807, 778216030845226561, 16027517577057849181, 344635879922587951321
Offset: 0
A347726
Expansion of e.g.f.: exp(x / (1-x)^x).
Original entry on oeis.org
1, 1, 1, 7, 37, 221, 1801, 15709, 157641, 1775521, 21898801, 296379931, 4346295757, 68682481141, 1163591541113, 21024039322441, 403559222086801, 8199021870113985, 175746277620520417, 3963144157484213359, 93778090395227788021, 2323080237693908254381
Offset: 0
-
a[0] = 1; a[n_] := n! * Sum[(-1)^(n - i) * Sum[i^j * StirlingS1[n - i - j, j]/(n - i - j)!, {j, 0, n - i}]/i!, {i, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Sep 11 2021 *)
-
a(n) = n!*sum(i=0, n, (-1)^(n-i)*sum(j=0, n-i, i^j*stirling(n-i-j, j, 1)/(n-i-j)!)/i!);
-
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^x)))
A362238
Expansion of e.g.f.: 1/(1 - x*(1+x)^x).
Original entry on oeis.org
1, 1, 2, 12, 60, 460, 3900, 39438, 456288, 5896224, 85230000, 1349017560, 23353941600, 437432418696, 8828284404576, 190867622500800, 4401749312069760, 107859517575659520, 2798352667710645120, 76636669899079699776, 2209235394261812751360
Offset: 0
A354612
Expansion of e.g.f. exp(f(x) - 1) where f(x) = (1 + x)^x = e.g.f. for A007113.
Original entry on oeis.org
1, 0, 2, -3, 32, -150, 1404, -11340, 120448, -1319976, 16600320, -223664760, 3300331704, -52223268240, 887583503520, -16071609481200, 309263446333440, -6296705309543040, 135262191966465600, -3056359409652695040, 72462969268541596800
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1+x)^x-1)))
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j!*sum(k=0, j\2, stirling(j-k, k, 1)/(j-k)!)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-4 of 4 results.