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A337798 Number of partitions of the n-th n-gonal pyramidal number into distinct n-gonal pyramidal numbers. 4
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 4, 5, 4, 5, 7, 11, 9, 4, 12, 12, 24, 23, 42, 59, 64, 58, 124, 206, 212, 168, 377, 539, 703, 873, 1122, 1505, 1943, 2724, 4100, 4513, 6090, 7138, 12079, 16584, 20240, 27162, 35874, 52622, 69817, 88059, 115628, 152756, 219538, 240200, 358733, 480674 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

Table of n, a(n) for n=0..61.

Eric Weisstein's World of Mathematics, Pyramidal Number

Index entries for sequences related to partitions

Index to sequences related to pyramidal numbers

FORMULA

a(n) = [x^p(n,n)] Product_{k=1..n} (1 + x^p(n,k)), where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.

EXAMPLE

a(9) = 2 because the ninth 9-gonal pyramidal number is 885 and we have [885] and [420, 266, 155, 34, 10].

MAPLE

p:= (n, k) ->  k * (k + 1) * (k * (n - 2) - n + 5) / 6:

f:= proc(n) local k, P;

  P:= mul(1+x^p(n, k), k=1..n);

  coeff(P, x, p(n, n));

end proc:

map(f, [$0..80]); # Robert Israel, Sep 23 2020

PROG

(PARI) default(parisizemax, 2^31);

p(n, k) = k*(k + 1)*(k*(n-2) - n + 5)/6;

a(n) = my(f=1+x*O(x^p(n, n))); for(k=1, n, f*=1+x^p(n, k)); polcoeff(f, p(n, n)); \\ Jinyuan Wang, Dec 21 2021

CROSSREFS

Cf. A006484, A288126, A298857, A337763, A337797, A337799.

Sequence in context: A306680 A083312 A032435 * A117502 A212630 A030360

Adjacent sequences:  A337795 A337796 A337797 * A337799 A337800 A337801

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 22 2020

EXTENSIONS

More terms from Robert Israel, Sep 23 2020

STATUS

approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)