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A182507 G.f.: Sum_{n>=0} n! * 2^(n*(n-1)/2) * x^n / Product_{k=1..n} (1 + k*2^k*x). 6
1, 1, 2, 12, 232, 12848, 1858464, 663242944, 562426769024, 1103780804371200, 4916976475489286656, 48986367134323580374016, 1078808700869188981508990976, 52024935094126934151475827453952, 5451309776848243787358722272838524928 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare the g.f. to the identities:

(1) 1/(1-x) = Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 + k*x).

(2) 1+x = Sum_{n>=0} 2^(n*(n-1)/2) * x^n / Product_{k=1..n} (1 + 2^k*x).

First differs from A309615 at a(5) = 12848, A309615(5) = 19230. - Gus Wiseman, Aug 11 2019

LINKS

Table of n, a(n) for n=0..14.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 232*x^4 + 12848*x^5 + 1858464*x^6 +...

such that

A(x) = 1 + x/(1+2*x) + 2!*2^1*x^2/((1+1*2*x)*(1+2*4*x)) + 3!*2^3*x^3/((1+1*2*x)*(1+2*4*x)*(1+3*8*x)) + 4!*2^6*x^4/((1+1*2*x)*(1+2*4*x)*(1+3*8*x)*(1+4*16*x)) +...

PROG

(PARI) {a(n)=polcoeff(sum(m=0, n, m!*2^(m*(m-1)/2)*x^m/prod(k=1, m, 1+k*2^k*x +x*O(x^n))), n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A005329, A182489, A309615.

Sequence in context: A013143 A009359 A011807 * A309615 A166316 A011840

Adjacent sequences:  A182504 A182505 A182506 * A182508 A182509 A182510

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 03 2012

STATUS

approved

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Last modified April 8 12:17 EDT 2020. Contains 333314 sequences. (Running on oeis4.)