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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 OFFSET 0,3 REFERENCES S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 10 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Sum_{k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.)