A261332 Expansion of Product_{k>=1} (1+x^k)^(A002203(k)).

1, 2, 7, 26, 83, 278, 894, 2848, 8947, 27844, 85774, 262090, 794802, 2393874, 7165622, 21327412, 63146545, 186063052, 545783103, 1594268778, 4638773567, 13447773510, 38850645513, 111874844146, 321166890522, 919314145044, 2624198013317, 7471158542418

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Asymptotics of the Euler transform of Fibonacci numbers, arXiv:1508.01796 [math.CO], Aug 07 2015

Eric Weisstein's World of Mathematics, Pell Number

Wikipedia, Pell number

Formula

a(n) ~ (1+sqrt(2))^n * exp(-1 + 2^(-3/2) + 2*sqrt(n) + s) / (2 * sqrt(Pi) * n^(3/4)), where s = Sum_{k>=2} = 2*(-1)^(k+1)/(((1+sqrt(2))^k + 2/(1 + (1+sqrt(2))^k) - 3)*k) = -0.2731939535370496116124191192900280854879921353977...

Mathematica

nmax=40; cPell[0]=2; cPell[1]=2; cPell[n_]:=cPell[n] = 2*cPell[n-1] + cPell[n-2]; CoefficientList[Series[Product[(1+x^k)^cPell[k], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A002203, A261329, A261330, A261331, A261050, A261051.

Sequence in context: A229241 A335179 A091145 * A220304 A363108 A300451

Adjacent sequences: A261329 A261330 A261331 * A261333 A261334 A261335

Keyword

nonn

Author

Vaclav Kotesovec, Aug 15 2015

Status

approved