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 A013619 Triangle of coefficients in expansion of (1+12x)^n. 1
 1, 1, 12, 1, 24, 144, 1, 36, 432, 1728, 1, 48, 864, 6912, 20736, 1, 60, 1440, 17280, 103680, 248832, 1, 72, 2160, 34560, 311040, 1492992, 2985984, 1, 84, 3024, 60480, 725760, 5225472, 20901888, 35831808, 1, 96, 4032, 96768, 1451520, 13934592, 83607552, 286654464, 429981696 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(n,k) equals the number of n-length words on {0,1,...,12} having n-k zeros. - Milan Janjic, Jul 24 2015 LINKS Table of n, a(n) for n=0..44. FORMULA G.f.: 1 / (1 - x(1+12y)). T(n,k) = 12^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*11^(n-i). Row sums are 13^n = A001022. - Mircea Merca, Apr 28 2012 EXAMPLE 1; 1, 12; 1, 24, 144; 1, 36, 432, 1728; 1, 48, 864, 6912, 20736; 1, 60, 1440, 17280, 103680, 248832; 1, 72, 2160, 34560, 311040, 1492992, 2985984; 1, 84, 3024, 60480, 725760, 5225472, 20901888, 35831808; MAPLE T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+12*x)^n): seq(T(n), n=0..10); # Alois P. Heinz, Jul 24 2015 MATHEMATICA Flatten[Table[CoefficientList[(1+12x)^n, x], {n, 0, 10}]] (* Harvey P. Dale, Oct 18 2015 *) CROSSREFS Sequence in context: A139724 A040155 A036185 * A092527 A085840 A276966 Adjacent sequences: A013616 A013617 A013618 * A013620 A013621 A013622 KEYWORD tabl,nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 8 19:26 EDT 2024. Contains 375754 sequences. (Running on oeis4.)