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 + ...
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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]
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 + ...
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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]
A307444
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, 0, 1, 2, 11, 54, 336, 2330, 18359, 161660, 1580853, 17031728, 200718372, 2569989304, 35531288796, 527506796282, 8368806193151, 141271243571640, 2527897717923387, 47789579768358498, 951677263953890739, 19910429474370487166, 436589745454529328720, 10012315468481417357976
Offset: 0
G.f.: A(x) = 1 + x^2 + 2*x^3 + 11*x^4 + 54*x^5 + 336*x^6 + 2330*x^7 + 18359*x^8 + 161660*x^9 + 1580853*x^10 + ...
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terms = 24; CoefficientList[1/x InverseSeries[Series[x/Sum[Subfactorial[k] x^k, {k, 0, terms}], {x, 0, terms}], x], x]
terms = 24; 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 = 24; A[] = 1; Do[A[x] = Sum[Subfactorial[k] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
Showing 1-3 of 3 results.