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A211196 a(n) = A211195(n-1)/n for n>=1. 1
1, 1, 2, 8, 48, 372, 3440, 36256, 423232, 5369184, 73051744, 1055835648, 16095734784, 257397846208, 4299558691968, 74762997772544, 1349551235537920, 25231125679907840, 487632516580187648, 9726238624438235136, 199929602149522450432, 4230081644094638877696 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..22.

FORMULA

G.f. satisfies: A(x) = Integral F(x) dx where F(x) is the g.f. of A211195 such that F(x) = 1 + 2*A(x*G(x)) and G(x) = F(x*G(x)). - Paul D. Hanna, Nov 21 2013

EXAMPLE

G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 48*x^5 + 372*x^6 + 3440*x^7 +...

The derivative of g.f. A(x) equals F(x), which is the g.f. of A211195 and begins:

F(x) = 1 + 2*x + 6*x^2 + 32*x^3 + 240*x^4 + 2232*x^5 + 24080*x^6 +...

where F(x) = 1 + 2*A(x*G(x)) and G(x) = F(x*G(x)):

G(x) = 1 + 2*x + 10*x^2 + 76*x^3 + 728*x^4 + 8104*x^5 + 100520*x^6 +...

PROG

(PARI) a(n)=local(F=1+2*x+sum(j=2, n-2, (j+1)*a(j+1)*x^j)+x*O(x^n)); if(n<1, 0, if(n==1, 1, 2*sum(k=0, n-2, polcoeff(F^(n-k-1), k)*polcoeff(F^(k+1)/(k+1), n-k-2))/n))

for(n=1, 25, print1(a(n), ", "))

(PARI) a(n)=local(B=1+x); for(i=1, n, B=1+2*subst(intformal(B), x, serreverse(x/B +x*O(x^n)))); polcoeff(intformal(B), n)

for(n=1, 25, print1(a(n), ", ")) \\ Paul D. Hanna, Nov 21 2013

CROSSREFS

Cf. A211195.

Sequence in context: A326887 A095989 A177388 * A334856 A219613 A124453

Adjacent sequences:  A211193 A211194 A211195 * A211197 A211198 A211199

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 03 2013

EXTENSIONS

Offset changed to 1 (from 0) by Paul D. Hanna, Nov 21 2013

STATUS

approved

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Last modified June 16 11:58 EDT 2021. Contains 345057 sequences. (Running on oeis4.)