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A090352 Satisfies A^3 = BINOMIAL(A)^2, where A = A090351^2. 4
1, 2, 7, 36, 255, 2370, 27713, 393352, 6582068, 126888632, 2767912036, 67362737168, 1808596304964, 53083358012760, 1690443996202428, 58039582729688320, 2136931230333535178, 83981145793974066484 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See comments in A090351.

LINKS

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

FORMULA

G.f. satisfies: A(x)^3 = A(x/(1-x))^2/(1-x)^2.

From Peter Bala, May 26 2015: (Start)

O.g.f. A(x) = exp( Sum_{n >= 1} b(n)*x^n/n ), where b(n) = Sum_{k = 1..n} k!*Stirling2(n,k)*2^k = A004123(n+1) = 2*A050351(n) for n >= 1. Cf. A084785.

BINOMIAL(A(x)) = exp( Sum_{n >= 1} c(n)*x^n/n ) where c(n) = (-1)^n*Sum_{k = 1..n} k!*Stirling2(n,k)*(-3)^k = A201339(n) = 3*A050351(n) for n >= 1.

A(x) = B(x)^2 and BINOMIAL(A(x)) = B(x)^3 where B(x) = 1 + x + 3*x^2 + 15*x^3 + 108*x^4 + ... is the o.g.f. for A090351. See also A019538. (End)

PROG

(PARI) {a(n)=local(A); if(n<1, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A^3+B^2); polcoeff(A, n, x))}

CROSSREFS

Cf. A090351; A004123, A019538, A050351, A084785, A201339.

Sequence in context: A249637 A259793 A112293 * A123549 A009704 A141308

Adjacent sequences:  A090349 A090350 A090351 * A090353 A090354 A090355

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Nov 26 2003

STATUS

approved

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)