A307402 G.f. A(x) satisfies: A(x) = Sum_{j>=0} j!*x^j*A(x)^j / Product_{k=1..j} (1 - k*x*A(x)).

1, 1, 4, 23, 164, 1362, 12792, 133891, 1550148, 19772030, 277054232, 4252637446, 71248226536, 1297226168708, 25542157054944, 541131735552507, 12275049552454916, 296787898215881990, 7617196890240489912, 206772478080888288082, 5917589117194665548600, 178040033221054576103036

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

G.f. A(x) satisfies: A(x) = Sum_{k>=0} A000670(k)*x^k*A(x)^k.

G.f.: A(x) = (1/x)*Series_Reversion(x/Sum_{k>=0} A000670(k)*x^k).

a(n) ~ n! / (log(2))^(n+1). - Vaclav Kotesovec, Apr 07 2019

Example

G.f.: A(x) = 1 + x + 4*x^2 + 23*x^3 + 164*x^4 + 1362*x^5 + 12792*x^6 + 133891*x^7 + 1550148*x^8 + 19772030*x^9 + 277054232*x^10 + ...

Mathematica

terms = 22; A[_] = 1; Do[A[x_] = Sum[j! x^j A[x]^j/Product[(1 - k x A[x]), {k, 1, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
terms = 22; A[_] = 1; Do[A[x_] = Sum[(1/2) HurwitzLerchPhi[1/2, -k, 0] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 22; CoefficientList[1/x InverseSeries[Series[x/Sum[(1/2) HurwitzLerchPhi[1/2, -k, 0]  x^k, {k, 0, terms}], {x, 0, terms}], x], x]

Crossrefs

Cf. A000670, A224922.

Sequence in context: A245110 A342988 A304074 * A354497 A111547 A171992

Adjacent sequences: A307399 A307400 A307401 * A307403 A307404 A307405

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2019

Status

approved