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A323323 G.f. Sum_{n>=0} ((1 + 2*x)^n - (1 + x)^n)^n. 1
1, 1, 4, 39, 508, 8651, 180541, 4462875, 127461499, 4129414609, 149614338010, 5994046983553, 263101175224096, 12555981779337615, 647278321588763668, 35845661666812566803, 2122283542537445564169, 133773419366606401021391, 8943959013589398905563475, 632203137717788438029869627, 47105820660836320646061788567, 3690081064592874994757245005533, 303181494230752217882627389578352 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n * n^n, where d = 1.406505772593750511415058484128041501018... and c = 0.485030515627129100167196305487639128... - Vaclav Kotesovec, Jan 14 2019
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 39*x^3 + 508*x^4 + 8651*x^5 + 180541*x^6 + 4462875*x^7 + 127461499*x^8 + 4129414609*x^9 + 149614338010*x^10 + ...
such that
A(x) = 1 + ((1+2*x)-(1+x)) + ((1+2*x)^2-(1+x)^2)^2 + ((1+2*x)^3-(1+x)^3)^3 + ((1+2*x)^4-(1+x)^4)^4 + ((1+2*x)^5-(1+x)^5)^5 + ...
PROG
(PARI) {a(n) = my(A=1, X=x+x*O(x^n)); A = sum(m=0, n, ((1 + 2*X)^m - (1 + X)^m)^m); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A068187 A307698 A319177 * A300188 A177775 A364981
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 11 2019
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)