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A215129 G.f.: Sum_{n>=0} d^n/dx^n (2*x + x^2)^(2*n) / n!. 1
1, 8, 108, 1604, 25000, 400680, 6539932, 108124704, 1804745052, 30345973020, 513246523504, 8722051475280, 148808353519644, 2547317293116512, 43729600850054640, 752553083643333008, 12978731348733064680, 224258766666165861192 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Compare to: Sum_{n>=0} d^n/dx^n x^(2*n)/n! = 1/sqrt(1-4*x).

LINKS

Table of n, a(n) for n=0..17.

FORMULA

G.f.: A(x) = d/dx G(x), where G(x) = x + (2*G(x) + G(x)^2)^2.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 12*x^2 + 64*x^3 + 370*x^4 + 2184*x^5 + 13132*x^6 +...

such that, by definition:

A(x) = 1 + d/dx (2*x+x^2)^2 + d^2/dx^2 (2*x+x^2)^4/2! + d^3/dx^3 (2*x+x^2)^6/3! + d^4/dx^4 (2*x+x^2)^8/4! + d^5/dx^5 (2*x+x^2)^10/5! +...

PROG

(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}

{a(n)=local(A=x); A=1+sum(m=1, n, Dx(m, (2*x+x^2+x*O(x^n))^(2*m)/m!)); polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A215128.

Sequence in context: A300807 A301446 A272497 * A234571 A120975 A193678

Adjacent sequences:  A215126 A215127 A215128 * A215130 A215131 A215132

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 04 2012

STATUS

approved

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Last modified October 7 14:13 EDT 2022. Contains 357271 sequences. (Running on oeis4.)