The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A296173 G.f. equals the logarithm of the e.g.f. of A296172. 6
 1, -3, -30, -2686, -517311, -173118807, -88535206152, -63977172334344, -61971659588102940, -77470793599569049440, -121439997599825393413344, -233353875172602479932391040, -539638027429765922735002220880, -1479049138515818646669055218090480, -4742815067612592169849894663392228480, -17597031102801426396121130730318359114880, -74817150772352720408567833273371047298417408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS E.g.f. G(x) of A296172 satisfies: [x^(n-1)] G(x)^(n^3) = [x^n] G(x)^(n^3) for n>=1. LINKS Paul D. Hanna, Table of n, a(n) for n = 1..180 FORMULA a(n) ~ -sqrt(1-c) * 3^(3*n - 3) * n^(2*n - 7/2) / (sqrt(2*Pi) * c^n * (3-c)^(2*n - 3) * exp(2*n)), where c = -LambertW(-3*exp(-3)) = -A226750. - Vaclav Kotesovec, Oct 13 2020 EXAMPLE G.f. A(x) = x - 3*x^2 - 30*x^3 - 2686*x^4 - 517311*x^5 - 173118807*x^6 - 88535206152*x^7 - 63977172334344*x^8 - 61971659588102940*x^9 - 77470793599569049440*x^10 - 121439997599825393413344*x^11 - 233353875172602479932391040*x^12 - 539638027429765922735002220880*x^13 - 1479049138515818646669055218090480*x^14 - 4742815067612592169849894663392228480*x^15 +... such that G(x) = exp(A(x)) = 1 + x - 5*x^2/2! - 197*x^3/3! - 65111*x^4/4! - 62390159*x^5/5! - 125012786669*x^6/6! - 447082993406405*x^7/7! - 2583111044504384687*x^8/8! - 22511408975342644804991*x^9/9! - 281350305428215911326408789*x^10/10! - 4850582201056517165575319399909*x^11/11! - 111834955668396093904661955538037255*x^12/12! +... satisfies [x^(n-1)] G(x)^(n^3) = [x^n] G(x)^(n^3) for n>=1. Series_Reversion(A(x)) = x + 3*x^2 + 48*x^3 + 3271*x^4 + 575163*x^5 + 185377116*x^6 + 93039467356*x^7 + 66505075585875*x^8 + 63970743282062646*x^9 + 79580632411431634441*x^10 + 124299284968805234137968*x^11 + 238188439678208173206500760*x^12 +...+ A295813(n)*x^n +... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^3)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^3 ); polcoeff(log(Ser(A)), n)} for(n=1, 30, print1(a(n), ", ")) CROSSREFS Cf. A296172, A295813, A296171, A296175, A296177. Sequence in context: A323819 A308228 A208789 * A248728 A115040 A296409 Adjacent sequences:  A296170 A296171 A296172 * A296174 A296175 A296176 KEYWORD sign AUTHOR Paul D. Hanna, Dec 07 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 12:24 EST 2020. Contains 338903 sequences. (Running on oeis4.)