A307441
G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 - x)^(k+1).
Original entry on oeis.org
1, 2, 7, 35, 216, 1527, 11927, 101056, 920055, 8960343, 93202418, 1035640333, 12305625141, 156513872514, 2131781868823, 31077520424879, 484157377851360, 8040920113043655, 141937291242762263, 2654252437895865112, 52412046969340405371, 1089506079309378596823
Offset: 0
G.f.: A(x) = 1 + 2*x + 7*x^2 + 35*x^3 + 216*x^4 + 1527*x^5 + 11927*x^6 + 101056*x^7 + 920055*x^8 + 8960343*x^9 + 93202418*x^10 + ...
-
terms = 22; A[] = 1; Do[A[x] = Sum[k! x^k A[x]^k/(1 - x)^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 22; A[] = 1; Do[A[x] = Sum[x^j Sum[k! Binomial[j, k] A[x]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
A307442
G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 - x*A(x))^(k+1).
Original entry on oeis.org
1, 2, 9, 54, 379, 2948, 24736, 220622, 2074775, 20491386, 212312349, 2310232488, 26473612772, 320735694048, 4126350096188, 56601987176510, 830233489763775, 13036492313617494, 218958840306428947, 3924128327446669670, 74779561501535316579, 1509296316416028136188
Offset: 0
G.f.: A(x) = 1 + 2*x + 9*x^2 + 54*x^3 + 379*x^4 + 2948*x^5 + 24736*x^6 + 220622*x^7 + 2074775*x^8 + 20491386*x^9 + 212312349*x^10 + ...
-
terms = 22; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[Floor[Exp[1] k!] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]
terms = 22; A[] = 1; Do[A[x] = Sum[k! x^k A[x]^k/(1 - x A[x])^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 22; A[] = 1; Do[A[x] = 1 + Sum[Floor[Exp[1] k!] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
A307443
G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x)^(k+1).
Original entry on oeis.org
1, 0, 1, 3, 14, 73, 439, 2986, 22849, 195639, 1864072, 19639587, 227216485, 2866190328, 39155468153, 575750407431, 9063067630294, 152007287492665, 2705337486885751, 50909087031293746, 1009776468826520181, 21052688394533433215, 460223336063328374304, 10525518902412521320567
Offset: 0
G.f.: A(x) = 1 + x^2 + 3*x^3 + 14*x^4 + 73*x^5 + 439*x^6 + 2986*x^7 + 22849*x^8 + 195639*x^9 + 1864072*x^10 + ...
-
terms = 24; A[] = 1; Do[A[x] = Sum[k! x^k A[x]^k/(1 + x)^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 24; A[] = 1; Do[A[x] = Sum[x^j Sum[(-1)^(j - k) k! Binomial[j, k] A[x]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
Showing 1-3 of 3 results.