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 A227468 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^3, n^2*k) * x^k ). 0
 1, 1, 2, 37, 1562313, 122131737394518, 26010968765974205465787541, 22347536974721066092798325076069521074882, 113454243067016764816945424312979214671918840299656114590507, 897202601035299299315214220213621062686601174611936477408260666612934393100592315294994 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare the definition to: exp( Sum_{n>=1} (1+y)^(n^3) * x^n/n ), which yields an integer series whenever y is an integer (e.g., A158110). Note: exp( Sum_{n>=1} (1+x)^(n^3) * x^n/n ) does not yield an integer series. LINKS Table of n, a(n) for n=0..9. EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 37*x^3 + 1562313*x^4 + 122131737394518*x^5 + ... such that the logarithm equals log(A(x)) = (1+x)*x + (1 + 70*x + x^2)*x^2/2 + (1 + 4686825*x + 4686825*x^2 + x^3)*x^3/3 + (1 + 488526937079580*x + 1832624140942590534*x^2 + 488526937079580*x^3 + x^4)*x^/4 + ... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m^3, m^2*k)*x^k)*x^m/m)+x*O(x^n)), n)} for(n=0, 15, print1(a(n), ", ")) CROSSREFS Cf. A158110, A206830, A227467. Sequence in context: A277409 A201556 A284309 * A049487 A163792 A050899 Adjacent sequences: A227465 A227466 A227467 * A227469 A227470 A227471 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 24 2013 STATUS approved

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Last modified November 30 06:48 EST 2023. Contains 367454 sequences. (Running on oeis4.)