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A022579 Expansion of Product_{m>=1} (1+x^m)^14. 2
1, 14, 105, 574, 2576, 10052, 35273, 113794, 342699, 974176, 2635955, 6833540, 17061345, 41197422, 96544003, 220212384, 490104727, 1066552228, 2273590095, 4755188704, 9771319068, 19751596934, 39317784863, 77150246040, 149357609184, 285497384004, 539227765104, 1006978117880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

FORMULA

a(n) ~ (7/6)^(1/4) * exp(Pi * sqrt(14*n/3)) / (256 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (14/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017

MATHEMATICA

nmax=50; CoefficientList[Series[Product[(1+q^m)^14, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)

PROG

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1+q^n)^14)) \\ G. C. Greubel, Feb 25 2018

(MAGMA) Coefficients(&*[(1+x^m)^14:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 25 2018

CROSSREFS

Column k=14 of A286335.

Sequence in context: A010966 A290895 A341226 * A061179 A285752 A076128

Adjacent sequences:  A022576 A022577 A022578 * A022580 A022581 A022582

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 25 13:19 EDT 2022. Contains 354851 sequences. (Running on oeis4.)