A325060 E.g.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n * exp(n^2*x) / A(x)^n.

1, 1, 2, 15, 148, 2565, 59046, 1825831, 70678280, 3343670217, 188213143690, 12380664239691, 937445644041996, 80731184378264173, 7828455595505947598, 847603141493494555695, 101732530008690207859216, 13451340197177805355768209, 1948644186311260903900163346, 307791516722206533702105826963, 52778747788778673408416550382100

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 15*x^3/3! + 148*x^4/4! + 2565*x^5/5! + 59046*x^6/6! + 1825831*x^7/7! + 70678280*x^8/8! + 3343670217*x^9/9! + 188213143690*x^10/10! + ...
such that
A(x) = 1 + x*exp(x)/A(x) + x^2*exp(2^2*x)/A(x)^2 + x^3*exp(3^2*x)/A(x)^3 + x^4*exp(4^2*x)/A(x)^4 + x^5*exp(5^2*x)/A(x)^5 + x^6*exp(6^2*x)/A(x)^6 + ...
Note that a(n) is divisible by n, for n >= 1, where a(n)/n starts
[1, 1, 5, 37, 513, 9841, 260833, 8834785, 371518913, 18821314369, ...].
RELATED SERIES.
log(A(x)) =  x + x^2/2! + 11*x^3/3! + 94*x^4/4! + 1849*x^5/5! + 42966*x^6/6! + 1385509*x^7/7! + 54885832*x^8/8! + 2654774721*x^9/9! + 152054810650*x^10/10! + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff( sum(m=0, #A, x^m * exp(m^2*x +x*O(x^n)) / Ser(A)^(m+1)), #A-1)); n!*A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A371582 A001854 A060226 * A002103 A191364 A308379

Adjacent sequences: A325057 A325058 A325059 * A325061 A325062 A325063

Keyword

nonn

Author

Paul D. Hanna, Apr 12 2019

Status

approved