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#16 by Russ Cox at Fri Mar 30 18:37:37 EDT 2012
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| AUTHOR
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_Paul D. Hanna (pauldhanna(AT)juno.com), _, Mar 05 2012
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Discussion
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| Fri Mar 30
| 18:37
| OEIS Server: https://oeis.org/edit/global/213
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#15 by Paul D. Hanna at Tue Mar 06 09:35:52 EST 2012
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#14 by Paul D. Hanna at Tue Mar 06 09:35:31 EST 2012
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#13 by Paul D. Hanna at Tue Mar 06 09:35:28 EST 2012
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| EXAMPLE
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wherein which the coefficients form A209330(n,k) = binomial(n^2, n*k).
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| STATUS
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proposed
editing
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#12 by Paul D. Hanna at Tue Mar 06 09:35:00 EST 2012
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#11 by Paul D. Hanna at Tue Mar 06 09:34:55 EST 2012
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| EXAMPLE
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TriangleThis triangle begins:
G.f.: A(x,y) = 1 + (1+y)*x + (1+4*y+y^2)*x^2 + (1+32*y+32*y^2+y^3)*x^3 + (1+487*y+3282*y^2+487*y^3+y^4)*x^4 +...
The logarithm of the g.f. equals the series:
log(A(x,y)) = (1 + y)*x
+ (1 + 6*y + y^2)*x^2/2
+ (1 + 84*y + 84*y^2 + y^3)*x^3/3
+ (1 + 1820*y + 12870*y^2 + 1820*y^3 + y^4)*x^4/4
+ (1 + 53130*y + 3268760*y^2 + 3268760*y^3 + 53130*y^4 + y^5)*x^5/5 +...
where the coefficients form A209330(n,k) = binomial(n^2, n*k).
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| CROSSREFS
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Cf. A209197, A167006, A206830, A209330 (log), A155200.
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| STATUS
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approved
editing
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#10 by Paul D. Hanna at Mon Mar 05 23:45:14 EST 2012
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#9 by Paul D. Hanna at Mon Mar 05 23:45:11 EST 2012
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#8 by Paul D. Hanna at Mon Mar 05 23:45:07 EST 2012
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| PROG
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(PARI) {T(n, k)=polcoeff(polcoeff(exp(sum(m=1, n, x^m/m*sum(kj=0, m, binomial(m^2, m*kj)*y^kj))+x*O(x^n)), n, x), k, y)}
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| STATUS
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approved
editing
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#7 by Paul D. Hanna at Mon Mar 05 23:36:25 EST 2012
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