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A179423 E.g.f. A(x) = F(x)^2 where F(x) is the e.g.f. of A179421. 2
1, 2, 10, 90, 1240, 23800, 598788, 18932620, 729558240, 33475442400, 1796086010400, 111058345494624, 7820581741096320, 621007886404464000, 55143814204485434400, 5436629250445000648800, 591426542480093093242368 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Let F(x) be the e.g.f. of A179421, then x*F(x) equals the e.g.f. of column 0 in the matrix log of the Riordan array (F(x), x*F(x)).
LINKS
FORMULA
a(n) = Sum_{k=0..n} C(n,k)*A179421(k)*A179421(n-k).
EXAMPLE
E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 90*x^3/3! + 1240*x^4/4! +...
The e.g.f. of A179421 is:
F(x) = 1 + x + 4*x^2/2! + 33*x^3/3! + 440*x^4/4! + 8380*x^5/5! +...
PROG
(PARI) {a(n)=local(A=1+2*x+sum(m=2, n-1, a(m)*x^m/m!)+x*O(x^n), B=truncate(sqrt(A+O(x^n)))); if(n<2, n!*polcoeff(A, n), n!*polcoeff((B+polcoeff(subst(x*B, x, x*B+x^2*O(x^n))/x, n)*x^n/(n-1)+x*O(x^n))^2, n))}
CROSSREFS
Cf. A179421.
Sequence in context: A198434 A326089 A277403 * A320962 A067550 A086587
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 28 2010
STATUS
approved

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Last modified June 17 10:05 EDT 2024. Contains 373445 sequences. (Running on oeis4.)