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A132683 a(n) = binomial(2^n + n, n). 3
1, 3, 15, 165, 4845, 435897, 131115985, 138432467745, 525783425977953, 7271150092378906305, 368539102493388126164865, 68777035446753808820521420545, 47450879627176629761462147774626305 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) = [x^n] 1/(1-x)^(2^n + 1).

G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)*n!). - Paul D. Hanna, Feb 25 2009

a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016

EXAMPLE

From Paul D. Hanna, Feb 25 2009: (Start)

G.f.: A(x) = 1 + 3*x + 15*x^2 + 165*x^3 + 4845*x^4 + 435897*x^5 + ...

A(x) = 1/(1-x) - log(1-2x)/(1-2x) + log(1-4x)^2/((1-4x)*2!) - log(1-8x)^3/((1-8x)*3!) +- ... (End)

MATHEMATICA

Table[Binomial[2^n+n, n], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)

PROG

(PARI) a(n)=binomial(2^n+n, n)

(PARI) {a(n)=polcoeff(sum(m=0, n, (-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))*m!)), n)} \\ Paul D. Hanna, Feb 25 2009

CROSSREFS

Cf. A060690, A132684.

Cf. A066384. - Paul D. Hanna, Feb 25 2009

Sequence in context: A015013 A269694 A153280 * A059386 A077792 A153079

Adjacent sequences:  A132680 A132681 A132682 * A132684 A132685 A132686

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 26 2007

STATUS

approved

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Last modified February 16 21:31 EST 2020. Contains 331975 sequences. (Running on oeis4.)