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A143184 Coefficients of a Ramanujan q-series. 1
1, 1, 2, 4, 6, 10, 15, 23, 33, 49, 69, 98, 136, 188, 256, 348, 466, 622, 824, 1084, 1418, 1846, 2389, 3077, 3947, 5038, 6407, 8115, 10241, 12876, 16141, 20160, 25110, 31179, 38609, 47674, 58724, 72141, 88421, 108114, 131902, 160565, 195061, 236468 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 10

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Sum_{k>=0} x^((k^2+k)/2) / ((1 - x) * (1 - x^2) ... (1 - x^k))^2.

EXAMPLE

1 + q + 2*q^2 + 4*q^3 + 6*q^4 + 10*q^5 + 15*q^6 + 23*q^7 + 33*q^8 + ...

MAPLE

b:= proc(n, i) option remember;

     `if`(i>n, 0, `if`(irem(n, i, 'r')=0, r, 0)+

      add(j*b(n-i*j, i+1), j=1..n/i))

    end:

a:= n-> `if`(n=0, 1, b(n, 1)):

seq(a(n), n=0..50);  # Alois P. Heinz, Oct 03 2018

PROG

(PARI) {a(n)= local(t); if( n<0, 0, t = 1 +x*O(x^n); polcoeff( sum(k=1, (sqrtint(8*n+1)-1)\2, t = t* x^k/ (1-x^k)^2 +x*O(x^n), 1), n))}

CROSSREFS

Convolution with A002448 is A132211.

Sequence in context: A073818 A239288 A306145 * A309173 A116084 A108925

Adjacent sequences:  A143181 A143182 A143183 * A143185 A143186 A143187

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 28 2008

STATUS

approved

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Last modified March 28 19:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)