The On-Line Encyclopedia of Integer Sequences (OEIS)

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A156335

G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.
(history; published version)

#2 by Russ Cox at Fri Mar 30 18:37:16 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Feb 10 2009

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#1 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

DATA

1, 2, 4, 16, 92, 1816, 47344, 4888640, 546663016, 245429690704, 113080892367776, 209848258185362560, 393950238751186551328, 2976605303522286162203456, 22642571073509592590956639360, 692351532949951721637759480882688

OFFSET

0,2

FORMULA

a(n) = (1/n)*Sum_{k=1..n} 2^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 4*x^2 + 16*x^3 + 92*x^4 + 1816*x^5 + 47344*x^6 +...

log(A(x)) = 2*x + 2^2*x^2/2 + 2^5*x^3/3 + 2^8*x^4/4 + 2^13*x^5/5 + 2^18*x^6/6 +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 2^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)}

CROSSREFS

Cf. A156334, A156336, A156337, A155200.

KEYWORD

nonn,new

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Feb 10 2009

STATUS

approved